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THE  ELECTRON 


THE  UNIVERSITY  OF  CHICAGO  PRESS 
CHICAGO,  ILLINOIS 


THE  BAKER  &  TAYLOR  COMPANY 

NEW   YORK 


THE  CAMBRIDGE  UNIVERSITY  PRESS 

LONDON  AND  EDINBURGH 

THE  MARUZEN-KABUSHIKI-KAISHA 

TOKYO,   OSAKA,    KYOTO,    FTTKUOKA,    SENDAI 

THE  MISSION  BOOK  COMPANY 

SHANGHAI 


THE   ELECTRON 

ITS  ISOLATION  AND  MEASUREMENT  AND  THE 

DETERMINATION  OF  SOME  OF 

ITS  PROPERTIES 


By 

ROBERT  ANDREWS  MILLIKAN 

Professor  of  Physics,  the  University  of  Chicago 


THE  UNIVERSITY  OF  CHICAGO  PRESS 
CHICAGO,  ILLINOIS 


COPYRIGHT  1917  BY 
THE  UNIVERSITY  OF  CHICAGO 


All  Rights  Reserved 


Published  August  1917 
Second  Impression  February  1918 
Third  Impression  November  1918 


Composed  and  Printed  By 

The  University  of  Chicago  Press 

Chicago,  Illinois,  U.S.A. 


GIFT 


TO 

ALBERT  A.  MICHELSON 

AND 
MARTIN  A.  RYERSON 

THIS  SMALL  OUTGROWTH  OF  THEIR 
INSPIRATION  AND  GENEROSITY 
IS  RESPECTFULLY  DEDICATED 


PREFACE 

It  is  hoped  that  this  volume  may  be  of  some  interest 
both  to  the  physicist  and  to  the  reader  of  somewhat  less 
technical  training.  It  has  been  thought  desirable  for 
the  sake  of  both  classes  of  readers,  not  to  break  the 
thread  of  the  discussion  in  the  body  of  the  book  with 
the  detailed  analyses  which  the  careful  student  demands. 
It  is  for  this  reason  that  all  mathematical  proofs  have 
been  thrown  into  appendixes.  If,  in  spite  of  this,  the 
general  student  finds  certain  chapters,  such  as  vii  and 
viii,  unintelligible,  it  is  hoped  that  without  them  he  may 
yet  gain  some  idea  of  certain  phases  at  least  of  the 

progress  of  modern  physics. 

R.  A.  MILLIKAN 
May  18,  1917 


CONTENTS 

INTRODUCTION      . 


I.  EARLY  VIEWS  OF  ELECTRICITY  .......        6 

II.  THE  EXTENSION  OF  THE  ELECTROLYTIC  LAWS  TO 
CONDUCTION  IN  GASES    .........       25 

III.  EARLY  ATTEMPTS  AT  THE  DIRECT  DETERMINATION 

OF  e       ..............       43 

IV.  GENERAL  PROOF  OF  THE  ATOMIC  NATURE  OF  ELEC- 
TRICITY      .............      64 

V.  THE  EXACT  EVALUATION  OF  e    ....          .     .       88 

yi.  THE  MECHANISM  OF  IONIZATION  OF  GASES  BY  X-RAYS 

AND  RADIUM  RAYS      ..........     123 

VII.  BROWNIAN  MOVEMENTS  IN  GASES  .     .          ...  142 

VIII.  THE  EXISTENCE  OF  A  SUB-ELECTRON  ?      .     .     .     .  155 

IX.  THE  STRUCTURE  OF  THE  ATOM   ......  179 

X.  THE  NATURE  OF  RADIANT  ENERGY       .....  217 

APPENDIX  A.    ne  FROM  MOBILITIES  AND  DIFFUSION   CO- 

EFFICIENTS      ............     239 

APPENDIX  B.    TOWNSEND'S  FIRST  ATTEMPT  AT  A  DETERMI- 

NATION OF  e     .......  ...     242 

APPENDIX  C.    THE  BROWNIAN-MOVEMENT  EQUATION  .     .     245 

APPENDIX  D.    THE  ENERTIA  OR  MASS  OF  AN  ELECTRICAL 

CHARGE  ON  A  SPHERE  OF  RADIUS  a      .....     249 

APPENDIX  E.    MOLECULAR    CROSS  -SECTION    AND    MEAN 

FREE  PATH      .........  252 

xi 


xii  CONTENTS 

PAGE 

APPENDIX  F.  NUMBER  OF  FREE  POSITIVE  ELECTRONS  IN 
THE  NUCLEUS  OF  AN  ATOM  BY  RUTHERFORD'S 
METHOD 254 

APPENDIX  G.    BOHR'S  THEORETICAL  DERIVATION  OF  THE 

VALUE  OF  THE  RYDBERG  CONSTANT 259 

APPENDIX  H.    THE  ELEMENTS,  THEIR  ATOMIC  NUMBERS, 

ATOMIC  WEIGHTS,  AND  CHEMICAL  POSITIONS  .     .     .     261 

INDEXES 265 


INTRODUCTION 

Perhaps  it  is  merely  a  coincidence  that  the  man  who 
first  noticed  that  the  rubbing  of  amber  would  induce 
in  it  a  new  and  remarkable  state  now  known  as  the 
state  of  electrification  was  also  the  man  who  first  gave 
expression  to  the  conviction  that  there  must  be  some 
great  unifying  principle  which  links  together  all  phe- 
nomena and  is  capable  of  making  them  rationally  intel- 
ligible; that  behind  all  the  apparent  variety  and  change 
of  things  there  is  some  primordial  element,  out  of  which 
all  things  are  made  and  the  search  for  which  must  be 
the  ultimate  aim  of  all  natural  science.  Yet  if  this  be 
merely  a  coincidence,  at  any  rate  to  Thales  of  Miletus 
must  belong  a  double  honor.  For  he  first  correctly 
conceived  and  correctly  stated,  as  far  back  as  600  B.C., 
the  spirit  which  has  actually  guided  the  development 
of  physics  in  all  ages,  and  he  also  first  described,  though 
in  a  crude  and  imperfect  way,  the  very  phenomenon  the 
study  of  which  has  already  linked  together  several  of 
the  erstwhile  isolated  departments  of  physics,  such  as 
radiant  heat,  light,  magnetism,  and  electricity,  and 
has  very  recently  brought  us  nearer  to  the  primordial 
element  than  we  have  ever  been  before. 

Whether  this  perpetual  effort  to  reduce  the  com- 
plexities of  the  world  to  simpler  terms,  and  to  build  up 
the  infinite  variety  of  objects  which  present  themselves 
to  our  senses  out  of  different  arrangements  or  motions  of 
the  least  possible  number  of  elementary  substances,  is  a 


2  THE  ELECTRON 

modern  heritage  from  Greek  thought,  or  whether  it  is  a 
native  instinct  of  the  human  mind  may  be  left  for  the 
philosopher  and  the  historian  to  determine.  Certain  it 
is,  however,  that  the  greatest  of  the  Greeks  aimed  at 
nothing  less  than  the  complete  banishment  of  caprice 
from  nature  and  the  ultimate  reduction  of  all  her  pro- 
cesses to  a  rationally  intelligible  and  unified  system. 
And  certain  it  is  also  that  the  periods  of  greatest  progress 
in  the  history  of  physics  have  been  the  periods  in  which 
this  effort  has  been  most  active  and  most  successful. 

Thus  the  first  half  of  the  nineteenth  century  is 
unquestionably  a  period  of  extraordinary  fruitfulness. 
It  is  at  the  same  time  a  period  in  which  for  the  first  time 
men,  under  Dalton's  lead,  began  to  get  direct,  experi- 
mental, quantitative  proof  that  the  atomic  world  which 
the  Greeks  had  bequeathed  to  us,  the  world  of  Leucippus 
and  Democritus  and  Lucretius,  consisting  as  it  did  of  an 
infinite  number  and  variety  of  atoms,  was  far  more  com- 
plex than  it  needed  to  be,  and  that  by  introducing  the 
idea  of  molecules  built  up  out  of  different  combinations 
and  groupings  of  atoms  the  number  of  necessary  elements 
could  be  reduced  to  but  about  seventy.  The  importance 
of  this  step  is  borne  witness  to  by  the  fact  that  out  of  it 
sprang  in  a  very  few  years  the  whole  science  of  modern 
chemistry. 

And  now  this  twentieth  century,  though  but  sixteen 
years  old,  has  already  attempted  to  take  a  still  bigger 
and  more  significant  step.  By  superposing  upon  the 
molecular  and  the  atomic  worlds  of  the  nineteenth  cen- 
tury a  third  electronic  world,  it  has  sought  to  reduce  the 
number  of  primordial  elements  to  not  more  than  two, 
namely,  positive  and  negative  electrical  charges,  Along 


INTRODUCTION  3 

with  this  effort  has  come  the  present  period  of  most 
extraordinary  development  and  fertility — a  period  in 
which  new  viewpoints  and  indeed  wholly  new  phenomena 
follow  one  another  so  rapidly  across  the  stage  of  physics 
that  the  actors  themselves  scarcely  know  what  is  happen- 
ing— a  period  too  in  which  the  commercial  and  industrial 
world  is  adopting  and  adapting  to  its  own  uses  with  a 
rapidity  hitherto  altogether  unparalleled  the  latest  prod- 
ucts of  the  laboratory  of  the  physicist  and  the  chemist. 
As  a  consequence,  the  results  of  yesterday's  researches, 
designed  for  no  other  purpose  than  to  add  a  little  more 
to  our  knowledge  of  the  ultimate  structure  of  matter,  are 
today  seized  upon  by  the  practical  business  world  and 
made  to  multiply  tenfold  the  effectiveness  of  the  tele- 
phone or  to  extract  six  times  as  much  light  as  was 
formerly  obtained  from  a  given  amount  of  electric  power. 
It  is  then  not  merely  a  matter  of  academic  interest 
that  electricity  has  been  proved  to  be  atomic  or  granular 
in  structure,  that  the  elementary  electrical  charge  has 
been  isolated  and  accurately  measured,  and  that  it  has 
been  found  to  enter  as  a  constitutent  into  the  making  of 
all  the  seventy-odd  atoms  of  chemistry.  These  are 
indeed  matters  of  fundamental  and  absorbing  interest  to 
the  man  who  is  seeking  to  unveil  nature's  inmost  secrets, 
but  they  are  also  events  which  are  pregnant  with  mean- 
ing for  the  man  of  commerce  and  for  the  worker  in  the 
factory.  For  it  usually  happens  that  when  nature's 
inner  workings  have  once  been  laid  bare,  man  sooner  or 
later  finds  a  way  to  put  his  brains  inside  the  machine  and 
to  drive  it  whither  he  wills.  Every  increase  in  man's 
knowledge  of  the  way  in  which  nature  works  must,  in 
the  long  run,  increase  by  just  so  much  man's  ability  to 


4  THE  ELECTRON 

control  nature  and  to  turn  her  hidden  forces  to  his  own 
account. 

The  purpose  of  this  volume  is  to  present  the  evidence 
for  the  atomic  structure  of  electricity,  to  describe  some 
of  the  most  significant  properties  of  the  elementary  elec- 
trical unit,  'the  electron,  and  to  discuss  the  bearing  of 
these  properties  upon  the  two  most  important  problems 
of  modern  physics:  the  structure  of  the  atom  and  the 
nature  of  electromagnetic  radiation.  In  this  presenta- 
tion I  shall  not  shun  the  discussion  of  exact  quantitative 
experiments,  for  it  is  only  upon  such  a  basis,  as  Pythago- 
ras asserted  more  than  two  thousand  years  ago,  that  any 
real  scientific  treatment  of  physical  phenomena  is  pos- 
sible. Indeed,  from  the  point  of  view  of  that  ancient 
philosopher,  the  problem  of  all  natural  philosophy  is  to 
drive  out  qualitative  conceptions  and  to  replace  them  by 
quantitative  relations.  And  this  point  of  view  has  been 
emphasized  by  the  farseeing  throughout  all  the  history  of 
physics  clear  down  to  the  present.  One  of  the  greatest 
of  modern  physicists,  Lord  Kelvin,  writes: 

When  you  can  measure  what  you  are  speaking  about  and 
express  it  in  numbers,  you  know  something  about  it,  and  when 
you  cannot  measure  it,  when  you  cannot  express  it  in  numbers, 
your  knowledge  is  of  a  meagre  and  unsatisfactory  kind.  It  may 
be  the  beginning  of  knowledge,  but  you  have  scarcely  in  your 
thought  advanced  to  the  stage  of  a  science. 

Although  my  purpose  is  to  deal  mostly  with  the 
researches  of  which  I  have  had  most  direct  and  intimate 
knowledge,  namely,  those  which  have  been  carried  on  dur- 
ing the  past  ten  years  in  this  general  field  in  the  Ryerson 
Laboratory,  I  shall  hope  to  be  able  to  give  a  correct  and 
just  review  of  the  preceding  work  out  of  which  these 


INTRODUCTION  5 

researches  grew,  as  well  as  of  parallel  work  carried  on  in 
other  laboratories.  In  popular  writing  it  seems  to  be 
necessary  to  link  every  great  discovery,  every  new  theory, 
every  important  principle,  with  the  name  of  a  single  indi- 
vidual. But  it  is  an  almost  universal  rule  that  develop- 
ments in  physics  actually  come  about  in  a  very  different 
way.  A  science,  like  a  planet,  grows  in  the  main  by  a 
process  of  infinitesimal  accretion.  Each  research  is 
usually  a  modification  of  a  preceding  one;  each  new 
theory  is  built  like  a  cathedral  through  the  addition  by 
many  builders  of  many  different  elements.  This  is  pre- 
eminently true  of  the  electron  theory.  It  has  been  a 
growth,  and  I  shall  endeavor  in  every  case  to  trace  the 
pedigree  of  each  research  connected  with  it. 


CHAPTER  I 

EARLY  VIEWS  OF  ELECTRICITY 
I.      GROWTH  OF  THE  ATOMIC  THEORY  OF  MATTER 

There  is  an  interesting  and  instructive  parallelism 
between  the  histories  of  the  atomic  conception  of  matter 
and  the  atomic  theory  of  electricity,  for  in  both  cases  the 
ideas  themselves  go  back  to  the  very  beginnings  of  the 
subject.  In  both  cases  too  these  ideas  remained  abso- 
lutely sterile  until  the  development  of  precise  quantita- 
tive methods  of  measurement  touched  them  and  gave 
them  fecundity.  It  took  two  thousand  years  for  this 
to  happen  in  the  case  of  the  theory  of  matter  and  one 
hundred  and  fifty  years  for  it  to  happen  in  the  case  of 
electricity;  and  no  sooner  had  it  happened  in  the  case  of 
both  than  the  two  domains  hitherto  thought  of  as  dis- 
tinct began  to  move  together  and  to  appear  as  perhaps 
but  different  aspects  of  one  and  the  same  phenomenon, 
thus  recalling  again  Thales'  ancient  belief  in  the  essential 
unity  of  nature.  How  this  attempt  at  union  has  come 
about  can  best  be  seen  by  a  brief  review  of  the  histories 
of  the  two  ideas. 

The  conception  of  a  world  made  up  of  atoms  which 
are  in  incessant  motion  was  almost  as  clearly  developed 
in  the  minds  of  the  Greek  philosophers  of  the  School  of 
Democritus  (420  B.C.),  Epicurus  (370  B.C.),  and  Lucre- 
tius (Roman,  50  B.C.)  as  it  is  in  the  mind  of  the  modern 
physicist,  but  the  idea  had  its  roots  in  one  case  in  a  mere 
speculative  philosophy;  in  the  other  case,  like  most  of 

6 


EARLY  VIEWS  OF  ELECTRICITY  7 

our  twentieth-century  knowledge,  it  rests  upon  direct, 
exact,  quantitative  observations  and  measurement.  Not 
that  the  human  eye  has  ever  seen  or  indeed  can  ever  see 
an  individual  atom  or  molecule.  This  is  forever  impos- 
sible, and  for  the  simple  reason  that  the  limitations  on  our 
ability  to  see  small  objects  are  imposed,  not  by  the  imper- 
fections of  our  instruments,  but  by  the  nature  of  the  eye 
itself,  or  by  the  nature  of  the  light-wave  to  which  the 
eye  is  sensitive.  If  we  are  to  see  molecules  our  biological 
friends  must  develop  wholly  new  types  of  eyes,  viz., 
eyes  which  are  sensitive  to  waves  one  thousand  times 
shorter  than  those  to  which  our  present  optic  nerves  can 
respond. 

But  after  all,  the  evidence  of  our  eyes  is  about  the 
least  reliable  kind  of  evidence  which  we  have.  We  are 
continually  seeing  things  which  do  not  exist,  even  though 
our  habits  are  unimpeachable.  It  is  the  relations  which 
are  seen  by  the  mind's  eye  to  be  the  logical  consequences 
of  exact  measurement  which  are  for  the  most  part 
dependable.  So  far  as  the  atomic  theory  of  matter  is 
concerned,  these  relations  have  all  been  developed  since 
1800,  so  that  both  the  modern  atomic  and  the  modern 
kinetic  theories  of  matter,  in  spite  of  their  great  an- 
tiquity, are  in  a  sense  less  than  one  hundred  years  old. 
Indeed,  nearly  all  of  our  definite  knowledge  about  mole- 
cules and  atoms  has  come  since  1851,  when  Joule1  in 
England  made  the  first  absolute  determination  of  a 
molecular  magnitude,  namely,  the  average  speed  with 
which  gaseous  molecules  of  a  given  kind  are  darting 
hither  and  thither  at  ordinary  temperatures.  This 

1  Mem.  of  the  Manchester  Lit.  and  Phil.  Soc.  (1851;  2d  series),  107; 
Phil.  Mag.,  XIV  (1857),  211. 


8  THE  ELECTRON 

result  was  as  surprising  as  many  others  which  have 
followed  in  the  field  of  molecular  physics,  for  it  showed 
that  this  speed,  in  the  case  of  the  hydrogen  molecule,  has 
the  stupendous  value  of  about  a  mile  a  second.  The 
second  molecular  magnitude  to  be  found  was  the  mean 
distance  a  molecule  of  a  gas  moves  between  collisions, 
technically  called  the  mean  free  path  of  a  molecule. 
This  was  computed  first  in  1860  by  Clerk  Maxwell.1  It 
was  also  1860  before  anyone  had  succeeded  in  making  any 
sort  of  an  estimate  of  the  number  of  molecules  in  a  cubic 
centimeter  of  a  gas.  When  we  reflect  that  we  can  now 
count  this  number  with  probably  greater  precision  than 
we  can  attain  in  determining  the  number  of  people  living 
in  New'York,  in  spite  of  the  fact  that  it  has  the  huge 
value  of  27.05  billion  billion,  one  gains  some  idea  of  how 
great  has  been  our  progress  in  mastering  some  at  least 
of  the  secrets  of  the  molecular  and  atomic  worlds.  The 
wonder  is  that  we  got  at  it  so  late.  Nothing  is  more  sur- 
prising to  the  student  brought  up  in  the  atmosphere  of 
the  scientific  thought  of  the  present  than  the  fact  that  the 
relatively  complex  and  intricate  phenomena  of  light  and 
electromagnetism  had  been  built  together  into  moder- 
ately consistent  and  satisfactory  theories  long  before  the 
much  simpler  phenomena  of  heat  and  molecular  physics 
had  begun  to  be  correctly  understood.  And  yet  almost 
all  the  qualitative  conceptions  of  the  atomic  and  kinetic 
theories  were  developed  thousands  of  years  ago.  Tyn- 
dall's  statement  of  the  principles  of  Democritus,  whom 
Bacon  considered  to  be  "a  man  of  mightier  metal  than 

1  Phil.  Mag.,  XIX  (1860;  4th  series),  28.  Clausius  had  discussed 
some  of  the  relations  of  this  quantity  in  1858  (Pogg.  Ann.,  CV  [1858], 
239),  but  Maxwell's  magnificent  work  on  the  viscosity  of  gases  first 
made  possible  its  evaluation. 


EARLY  VIEWS  OF  ELECTRICITY  9 

Plato  or  Aristotle,  though  their  philosophy  was  noised  and 
celebrated  in  the  schools  amid  the  din  and  pomp  of  pro- 
fessors/' will  show  how  complete  an  atomic  philosophy 
had  arisen  400  years  B.C.  "That  it  was  entirely  de- 
stroyed later  was  not  so  much  due  to  the  attacks  upon 
it  of  the  idealistic  school,  whose  chief  representatives  were 
Plato  and  Aristotle,  as  to  the  attacks  upon  all  civiliza- 
tion of  Genseric,  Attila,  and  the  barbarians."  That  the 
Aristotelian  philosophy  lasted  throughout  this  period  is 
explained  by  Bacon  thus:  "At  a  time  when  all  human 
learning  had  suffered  shipwreck  these  planks  of  Aris- 
totelian and  Platonic  Philosophy,  as  being  of  a  lighter 
and  more  inflated  substance,  were  preserved  and  came 
down  to  us,  while  things  more  solid  sank  and  almost 
passed  into  oblivion." 

Democritus'  principles,  as  quoted  by  Tyndall,  are  as 
follows : 

1.  From  nothing  comes  nothing.    Nothing  that  exists  can  be 
destroyed.     All  changes  are  due  to  the  combination  and  separation 
of  molecules. 

2.  Nothing  happens  by  chance.    Every  occurrence  has  its 
cause  from  which  it  follows  by  necessity. 

3.  The  only  existing  things  are  the  atoms  and  empty  space; 
all  else  is  mere  opinion. 

4.  The  atoms  are  infinite  in  number  and  infinitely  various  in 
form;  they  strike  together  and  the  lateral  motions  and  whirlings 
which  thus  arise  are  the  beginnings  of  worlds. 

5.  The  varieties  of  all  things  depend  upon  the  varieties  of 
their  atoms,  in  number,  size,  and  aggregation. 

6.  The  soul  consists  of  fine,  smooth,  round  atoms  like  those 
of  fire.    These  are  the  most  mobile  of  all.    They  interpenetrate 
the  whole  body  and  in  their  motions  the  phenomena  of  life  arise. 

These  principles  with  a  few  modifications  and  omis- 
sions might  almost  pass  muster  today.  The  great 
advance  which  has  been  made  in  modern  times  is  not  so 


io  THE  ELECTRON 

much  in  the  conceptions  themselves  as  in  the  kind  of 
foundation  upon  which  the  conceptions  rest.  The  prin- 
ciples enumerated  above  were  simply  the  opinions  of  one 
man  or  of  a  school  of  men.  There  were  scores  of  other 
rival  opinions,  and  no  one  could  say  which  was  the  better. 
Today  there  is  absolutely  no  philosophy  in  the  field  other 
than  the  atomic  philosophy,  at  least  among  physicists. 
Yet  this  statement  could  not  have  been  made  even  as 
much  as  ten  years  ago.  For  in  spite  of  all  the  multiple 
relationships  between  combining  powers  of  the  elements, 
and  in  spite  of  all  the  other  evidences  of  chemistry  and 
nineteenth-century  physics,  a  group  of  the  foremost  of 
modern  thinkers,  until  quite  recently,  withheld  their 
allegiance  from  these  theories.  The  most  distinguished 
of  this  group  was  the  German  chemist  and  philosopher, 
Wilhelm  Ostwald.  However,  in  the  preface  to  a  new 
edition  of  his  Outlines  of  Chemistry  he  now  makes  the 
following  clear  and  frank  avowal  of  his  present  position 
He  says: 

I  am  now  convinced  that  we  have  recently  become  possessed 
of  experimental  evidence  of  the  discrete  or  grained  nature  of 
matter  for  which  the  atomic  hypothesis  sought  in  vain  for  hun- 
dreds and  thousands  of  years".  The  isolation  and  counting  of 
gaseous  ions  on  the  one  hand  ....  and  on  the  other  the  agree- 
ment of  the  Brownian  movements  with  the  requirements  of  the 
kinetic  hypothesis  ....  justify  the  most  cautious  scientist  in 
now  speaking  of  the  experimental  proof  of  the  atomic  theory  of 
matter.  The  atomic  hypothesis  is  thus  raised  to  the  position  of 
a  scientifically  well-founded  theory. 

II.      GROWTH  OF  ELECTRICAL  THEORIES 

The  granular  theory  of  electricity,  while  unlike  the 
atomic  and  kinetic  theories  of  matter  in  that  it  can  boast 


EARLY  VIEWS  OF  ELECTRICITY  n 

no  great  antiquity  in  any  form,  is  like  them  in  that  the 
first  man  who  speculated  upon  the  nature  of  electricity  at 
all  conceived  of  it  as  having  an  atomic  structure.  Yet  it 
is  only  within  very  recent  years — twenty  at  the  most — 
that  the  modern  electron  theory  has  been  developed. 
There  are  no  electrical  theories  of  any  kind  which  go 
back  of  Benjamin  Franklin  (1750).  Aside  from  the  dis- 
covery of  the  Greeks  that  rubbed  amber  had  the  power 
of  attracting  to  itself  light  objects,  there  was  no  knowl- 
edge at  all  earlier  than  1600  A.D.,  when  Gilbert,  Queen 
Elizabeth's  surgeon,  and  a  scientist  of  great  genius  and 
insight,  found  that  a  glass  rod  and  some  twenty  other 
bodies,  when  rubbed  with  silk,  act  like  the  rubbed  amber 
of  the  Greeks,  and  he  consequently  decided  to  describe 
the  phenomenon  by  saying  that  the  glass  rod  had  become 
electrified  (amberized,  electron  being  the  Greek  word  for 
amber),  or,  as  we  now  say,  had  acquired  a  charge  of 
electricity.  In  1733  Dufay,  a  French  physicist,  further 
found  that  sealing  wax,  when  rubbed  with  cat's  fur,  was 
also  electrified,  but  that  it  differed  from  the  electrified 
glass  rod,  in  that  it  strongly  attracted  any  electrified  body 
which  was  repelled  by  the  glass,  while  it  repelled  any 
electrified  body  which  was  attracted  by  the  glass.  He 
was  thus  led  to  recognize  two  kinds  of  electricity,  which 
he  termed  " vitreous"  and  " resinous."  About  1747 
Benjamin  Franklin,  also  recognizing  these  two  kinds  of 
electrification,  introduced  the  terms  "positive"  and 
"negative,"  to  distinguish  them.  Thus,  he  said,  we  will 
arbitrarily  call  any  body  positively  electrified  if  it  is 
repelled  by  a  glass  rod  which  has  been  rubbed  with  silk, 
and  we  will  call  any  body  negatively  electrified  if  it  is 
repelled  by  sealing  wax  which  has  been  rubbed  with  cat's 


12  THE  ELECTRON 

fur.  These  are  today  our  definitions  of  positive  and  nega- 
tive electrical  charges.  Notice  that  in  setting  them  up  we 
propose  no  theory  whatever  of  electrification,  but  con- 
tent ourselves  simply  with  describing  the-  phenomena. 

In  the  next  place  it  was  surmised  by  Franklin  and 
indeed  asserted  by  him  in  the  very  use  of  the  terms 
"positive"  and  "negative,"  although  the  accurate  proof 
of  the  relation  was  not  made  until  the  time  of  Faraday's 
ice-pail  experiment  in  1837,  that  when  glass  is  positively 
electrified  by  rubbing  it  with  silk,  the  silk  itself  takes  up 
a  negative  charge  of  exactly  the  same  amount  as  the 
positive  charge  received  by  the  glass,  and,  in  general, 
that  positive  and  negative  electrical  charges  always  appear 
simultaneously  and  in  exactly  equal  amounts. 

So  far,  still  no  theory.  But  in  order  to  have  a 
rational  explanation  of  the  phenomena  so  far  considered, 
particularly  this  last  one,  Franklin  now  made  the  assump- 
tion that  something  which  he  chose  to  call  the  electrical 
fluid  or  "electrical  fire"  exists  in  normal  amount  as  a  con- 
stituent of  all  matter  in  the  neutral,  or  unelectrified  state, 
and  that  more  than  the  normal  amount  in  any  body  is 
manifested  as  a  positive  electrical  charge,  and  less  than 
the  normal  amount  as  a  negative  charge.  Aepinus,  pro- 
fessor of  physics  at  St.  Petersburg  and  an  admirer  of 
Franklin's  theory,  pointed  out  that,  in  order  to  account 
for  the  repulsion  of  two  negatively  electrified  bodies,  it 
was  necessary  to  assume  that  matter,  when  divorced  from 
Franklin's  electrical  fluid,  was  self-repellent,  i.e.,  that  it 
possessed  properties  quite  different  from  those  which  are 
found  in  ordinary  unelectrified  matter.  In  order,  how- 
ever, to  leave  matter,  whose  independent  existence  was 
thus  threatened,  endowed  with  its  familiar  old  properties, 


EARLY  VIEWS  OF  ELECTRICITY  13 

and  in  order  to  get  electrical  phenomena  into  a  class  by 
themselves,  other  physicists  of  the  day,  led  by  Symmer, 
1759,  preferred  to  assume  that  matter  in  a  neutral  state 
shows  no  electrical  properties  because  it  contains  as  con- 
stituents equal  amounts  of  two  weightless  fluids  which  they 
called  positive  and  negative  electricity,  respectively.  From 
this  point  of  view  a  positively  charged  body  is  one  in 
which  there  is  more  of  the  positive  fluid  than  of  the  nega- 
tive, and  a  negatively  charged  body  is  one  in  which  the 
negative  fluid  is  in  excess. 

Thus  arose  the  so-called  two-fluid  theory — a  theory 
which  divorced  again  the  notions  of  electricity  and  mat- 
ter after  Franklin  had  taken  a  step  toward  bringing  them 
together.  This  theory,  in  spite  of  its  intrinsic  difficulties, 
dominated  the  development  of  electrical  science  for  one 
hundred  years  and  more.  This  was  because,  if  one  did 
not  bother  himself  much  with  the  underlying  physical 
conception,  the  theory  lent  itself  admirably  to  the 
description  of  electrical  phenomena  and  also  to  mathe- 
matical formulation.  Further,  it  was  convenient  for  the 
purposes  of  classification.  It  made  it  possible  to  treat 
electrical  phenomena  in  a  category  entirely  by  them- 
selves, without  raising  any  troublesome  questions  as  to 
the  relation,  for  example,  between  electrical  and  gravita- 
tional or  cohesive  forces.  But  in  spite  of  these  advan- 
tages it  was  obviously  a  makeshift.  For  the  notion  of 
two  fluids  which  could  exert  powerful  forces  and  yet 
which  were  absolutely  without  weight — the  most  funda- 
mental of  physical  properties — and  the  further  notion  of 
two  fluids  which  had  no  physical  properties  whatever, 
that  is,  which  disappeared  entirely  when  they  were 
mixed  in  equal  proportions — these  notions  were  in  a 


14  THE  ELECTRON 

high  degree  non-physical.  Indeed,  J.  J.  Thomson 
remarked  in  his  Silliman  Lectures  in  1903  that 

the  physicists  and  mathematicians  who  did  most  to  develop  the 
fluid  theories  confined  their  attention  to  questions  which  involved 
only  the  law  of  forces  between  electrified  bodies  and  the  simulta- 
neous production  of  equal  quantities  of  plus  and  minus  electricity, 
and  refined  and  idealized  their  conception  of  the  fluids  themselves 
until  any  reference  to  their  physical  properties  was  considered 
almost  indelicate. 

From  the  point  of  view  of  economy  in  hypothesis, 
Franklin's  one-fluid  theory,  as  modified  by  Aepinus,  was 
the  better.  Mathematically  the  two  theories  were  iden- 
tical. The  differences  may  be  summed  up  thus.  The 
modified  one-fluid  theory  required  that  matter,  when 
divorced  from  the  electrical  fluid,  have  exactly  the  same 
properties  which  the  two-fluid  theory  ascribed  to  nega- 
tive electricity,  barring  only  the  property  of  fluidity. 
So  that  the  most  important  distinction  between  the 
theories  was  that  the  two-fluid  theory  assumed  the  exist- 
ence of  three  distinct  entities,  named  positive  electricity, 
negative  electricity,  and  matter,  while  the  one-fluid 
theory  reduced  these  three  entities  to  two,  which  Franklin 
called  matter  and  electricity,  but  which  might  perhaps  as 
well  have  been  called  positive  electricity  and  negative 
electricity,  unelectrified  matter  being  reduced  to  a  mere 
combination  of  these  two. 

Of  course,  the  idea  of  a  granular  structure  for  elec- 
tricity was  foreign  to  the  two-fluid  theory,  and  since  this 
dominated  the  development  of  electrical  science,  there 
was  seldom  any  mention  in  connection  with  it  of  an  elec- 
trical atom,  even  as  a  speculative  entity.  But  with 
Franklin  the  case  was  different.  His  theory  was  essen- 


EARLY  VIEWS  OF  ELECTRICITY  15 

tially  a  material  one,  and  he  unquestionably  believed  in 
the  existence  of  an  electrical  particle  or  atom,  for  he  says : 
"The  electrical  matter  consists  of  particles  extremely 
subtle,  since  it  can  permeate  common  matter,  even  the 
densest,  with  such  freedom  and  ease  as  not  to  receive  any 
appreciable  resistance."  When  Franklin  wrote  that, 
however,  he  could  scarcely  have  dreamed  that  it  would 
ever  be  possible  to  isolate  and  study  by  itself  one  of 
the  ultimate  particles  of  the  electrical  fluid.  The 
atomic  theory  of  electricity  was  to  him  what  the 
atomic  theory  of  matter  was  to  Democritus,  a  pure 
speculation. 

The  first  bit  of  experimental  evidence  which  appeared 
in  its  favor  came  in  1833,  when  Faraday  found  that  the 
passage  of  a  given  quantity  of  electricity  through  a  solu- 
tion containing  a  compound  of  hydrogen,  for  example, 
would  always  cause  the  appearance  at  the  negative 
terminal  of  the  same  amount  of  hydrogen  gas  irrespec- 
tive of  the  kind  of  hydrogen  compound  which  had  been 
dissolved,  and  irrespective  also  of  the  strength  of  the 
solution;  that,  further,  the  quantity  of  electricity 
required  to  cause  the  appearance  of  one  gram  of  hydro- 
gen would  always  deposit  from  a  solution  containing 
silver  exactly  107 .  i  grams  of  silver.  This  meant,  since 
the  weight  of  the  silver  atom  is  exactly  107 .  i  times  the 
weight  of  the  hydrogen  atom,  that  the  hydrogen  atom 
and  the  silver  atom  are  associated  in  the  solution  with 
exactly  the  same  quantity  of  electricity.  When  it  was 
further  found  in  this  way  that  all  atoms  which  are 
univalent  in  chemistry,  that  is,  which  combine  with  one 
atom  of  hydrogen,  carry  precisely  the  same  quantity  of 
electricity,  and  all  atoms  which  are  bivalent  carry  twice 


1 6  THE  ELECTRON 

this  amount,  and,  in  general,  that  valency,  in  chemistry, 
is  always  exactly  proportional  to  the  quantity  of  elec- 
tricity carried  by  the  atom  in  question,  it  was  obvious 
that  the  atomic  theory  of  electricity  had  been  given  very 
strong  support. 

But  striking  and  significant  as  were  these  discoveries, 
they  did  not  serve  at  all  to  establish  the  atomic  hypothe- 
sis of  the  nature  of  electricity.  They  were  made  at  the 
very  time  when  attention  began  to  be  directed  strongly 
away  from  the  conception  of  electricity  as  a  substance 
of  any  kind,  and  it  was  no  other  than  Faraday  himself 
who,  in  spite  of  the  brilliant  discoveries  just  mentioned, 
started  this  second  period  in  the  development  of  electrical 
theory,  a  period  lasting  from  1840  to  about  1900.  In 
this  period  electrical  phenomena  are  almost  exclusively 
thought  of  in  terms  of  stresses  and  strains  in  the  medium 
which  surrounds  the  electrified  body.  Up  to  this  time 
a  more  or  less  definite  something  called  a  charge  of  elec- 
tricity had  been  thought  of  as  existing  on  a  charged  body 
and  had  been  imagined  to  exert  forces  on  other  charged 
bodies  at  a  distance  from  it  in  quite  the  same  way  in 
which  the  gravitational  force  of  the  earth  acts  on  the 
moon  or  that  of  the  sun  on  the  earth.  This  notion  of 
action  at  a  distance  was  repugnant  to  Faraday,  and  he 
found  in  the  case  of  electrical  forces  experimental  reasons 
for  discarding  it  which  had  not  then,  nor  have  they  as  yet, 
been  found  in  the  case  of  gravitational  forces.  These 
reasons  are  summed  up  in  the  statement  that  the  electri- 
cal force  between  two  charged  bodies  is  found  to  depend 
on  the  nature  of  the  intervening  medium,  while  gravita- 
tional pulls  are,  so  far  as  is  known,  independent  of  inter- 
vening bodies.  Faraday,  therefore,  pictured  to  himself 


EARLY  VIEWS  OF  ELECTRICITY  17 

the  intervening  medium  as  transmitting  electrical  force 
in  quite  the  same  way  in  which  an  elastic  deformation 
started  at  one  end  of  a  rod  is  transmitted  by  the  rod. 
Further,  since  electrical  forces  act  through  a  vacuum, 
Faraday  had  to  assume  that  it  is  the  ether  which  acts  as 
the  transmitter  of  these  electrical  stresses  and  strains. 
The  properties  of  the  ether  were  then  conceived  of  as 
modified  by  the  presence  of  matter  in  order  to  account 
for  the  fact  that  the  same  two  charges  attract  each  other 
with  different  forces  according  as  the  intervening  medium 
is,  for  example,  glass,  or  ebonite,  or  air,  or  merely  ether. 
These  views,  conceived  by  Faraday  and  put  into  mathe- 
matical form  by  Maxwell,  called  attention  away  from 
the  electrical  phenomena  in  or  on  a  conductor  carrying 
electricity  and  focused  it  upon  the  stresses  and  strains 
taking  place  in  the  medium  about  the  conductor.  When 
in  T886  Heinrich  Hertz  in  Bonn,  Germany,  proved  by 
direct  experiment  that  electrical  forces  are  indeed  trans- 
mitted in  the  form  of  electric  waves,  which  travel  through 
space  with  the  speed  of  light  exactly  as  the  Faraday- 
Maxwell  theory  had  predicted,  the  triumph  of  the 
ether-stress  point  of  view  was  complete.  Thereupon 
textbooks  were  written  by  enthusiastic,  but  none  too 
cautious,  physicists  in  which  it  was  asserted  that  an 
electric  charge  is  nothing  more  than  a  "  state  of  strain 
in  the  ether,"  and  an  electric  current,  instead  of  repre- 
senting the  passage  of  anything  definite  along  the  wire, 
corresponds  merely  to  a  continuous  "slip"  or  "break- 
down of  a  strain"  in  the  medium  within  the  wire. 
Lodge's  book,  Modern  Views  of  Electricity,  has  been  the 
most  influential  disseminator  and  expounder  of  this 
point  of  view. 


1 8  THE  ELECTRON 

Now  what  had  actually  been  proved  was  not  that 
electricity  is  a  state  of  strain,  but  that  when  any  elec- 
trical charge  appears  upon  a  body  the  medium  about  the 
body  does  indeed  become  the  seat  of  new  forces  which 
are  transmitted  through  the  medium,  like  any  elastic 
forces,  with  a  definite  speed.  Hence  it  is  entirely  proper 
to  say  that  the  medium  about  a  charged  body  is  in  a 
state  of  strain.  But  it  is  one  thing  to  say  that  the  elec- 
trical charge  on  the  body  produces  a  state  of  strain  in  the 
surrounding  medium,  and  quite  another  thing  to  say  that 
the  electrical  charge  is  nothing  but  a  state  of  strain  in  the 
surrounding  medium,  just  as  it  is  one  thing  to  say  that 
when  a  man  stands  on  a  bridge  he  produces  a  mechanical 
strain  in  the  timbers  of  the  bridge,  and  another  thing  to 
say  that  the  man  is  nothing  more  than  a  mechanical 
strain  in  the  bridge.  The  practical  difference  between 
the  two  points  of  view  is  that  in  the  one  case  you  look 
for  other  attributes  of  the  man  besides  the  ability  to 
produce  a  strain  in  the  bridge,  and  in  the  other  case  you 
do  not  look  for  other  attributes.  So  the  strain  theory, 
although  not  irreconcilable  with  the  atomic  hypothesis, 
was  actually  antagonistic  to  it,  because  it  led  men  to 
think  of  the  strain  as  distributed  continuously  about  the 
surface  of  the  charged  body,  rather  than  as  radiating  from 
definite  spots  or  centers  peppered  over  the  surface  of  the 
body.  Between  1833  and  1900,  then,  the  physicist  was 
in  this  peculiar  position:  when  he  was  thinking  of  the 
passage  of  electricity  through  a  solution,  he  for  the  most 
part,  following  Faraday,  pictured  to  himself  definite 
specks  or  atoms  of  electricity  as  traveling  through  the 
solution,  each  atom  of  matter  carrying  an  exact  multiple, 
which  might  be  anywhere  between  one  and  eight,  of  q 


EARLY  VIEWS  OF  ELECTRICITY  19 

definite  elementary  electrical  atom,  while,  when  he  was 
thinking  of  the  passage  of  a  current  through  a  metallic 
conductor,  he  gave  up  altogether  the  atomic  hypothesis, 
and  attempted  to  picture  the  phenomenon  to  himself  as 
a  continuous  "slip"  or  "breakdown  of  a  strain"  in  the 
material  of  the  wire.  In  other  words,  he  recognized  two 
types  of  electrical  conduction  which  were  wholly  distinct 
in  kind — electrolytic  conduction  and  metallic  conduction ; 
and  since  more  of  the  problems  of  the  physicist  dealt  with 
metallic  than  with  electrolytic  conduction,  the  atomic 
conception,  as  a  general  hypothesis,  was  almost,  though 
not  quite,  unheard  of.  Of  course  it  would  be  unjust  to 
the  thinkers  of  this  period  to  say  that  they  failed  to 
recognize  and  appreciate  this  gulf  between  current  views 
as  to  the  nature  of  electrolytic  and  metallic  conduction, 
and  simply  ignored  the  difficulty.  This  they  did  not  do, 
but  they  had  all  sorts  of  opinions  as  to  the  causes. 
Maxwell  himself  in  his  text  on  Electricity  and  Magnetism, 
published  in  1873,  recognizes,  in  the  chapter  on  "Elec- 
trolysis,"1 the  significance  of  Faraday's  laws,  and  even 
goes  so  far  as  to  say  that  "for  convenience  in  description 
we  may  call  this  constant  molecular  charge  (revealed  by 
Faraday's  experiments)  one  molecule  of  electricity." 
Nevertheless,  a  little  farther  on  he  repudiates  the  idea 
that  this  term  can  have  any  physical  significance  by 
saying  that  "it  is  extremely  improbable  that  when  we 
come  to  understand  the  true  nature  of  electrolysis  we 
shall  retain  in  any  form  the  theory  of  molecular  charges, 
for  then  we  shall  have  obtained  a  secure  basis  on  which 
to  form  a  true  theory  of  electric  currents  and  so  become 
independent  of  these  provisional  hypotheses." 

1  I,  375-36. 


20  THE  ELECTRON 

And  as  a  matter  of  fact,  Faraday's  experiments  had 
not  shown  at  all  that  electrical  charges  on  metallic  con- 
ductors consist  of  specks  of  electricity,  even  though  they 
had  shown  that  the  charges  on  ions  in  solutions  have 
definite  values  which  are  always  the  same  for  univalent 
ions.  It  was  entirely  logical  to  assume,  as  Maxwell  did, 
that  an  ion  took  into  solution  a  definite  quantity  of  elec- 
tricity because  of  some  property  which  it  had  of  always 
charging  up  to  the  same  amount  from  a  charged  plate. 
There  was  no  reason  for  assuming  the  charge  on  the  elec- 
trode to  be  made  up  of  some  exact  number  of  electrical 
atoms. 

On  the  other  hand,  Wilhelm  Weber,  in  papers  written 
in  187  1,1  built  up  his  whole  theory  of  electromagnetism 
on  a  basis  which  was  practically  identical  with  the  modi- 
fied Franklin  theory  and  explained  all  the  electrical 
phenomena  exhibited  by  conductors,  including  thermo- 
electric and  Peltier  effects,  on  the  assumption  of  two 
types  of  electrical  constituents  of  atoms,  one  of  which  was 
very  much  more  mobile  than  the  other.  Thus  the  hypo- 
thetical molecular  current,  which  Ampere  had  imagined 
fifty  years  earlier  to  be  continually  flowing  inside  of 
molecules  and  thereby  rendering  these  molecules  little 
electromagnets,  Weber  definitely  pictures  to  himself 
as  the  rotation  of  light,  positive  charges  about  heavy 
negative  ones.  His  words  are: 

The  relation  of  the  two  particles  as  regards  their  motions  is 
determined  by  the  ratio  of  their  masses  e  and  e',  on  the  assumption 
that  in  e  and  e'  are  included  the  masses  of  the  ponderable  atoms 
which  are  attached  to  the  electrical  atoms.  Let  e  be  the  positive 
electrical  particle.  Let  the  negative  be  exactly  equal  and  opposite 


See  Werfc?,  IV,  281. 


EARLY  VIEWS  OF  ELECTRICITY  2t 

and  therefore  denoted  by  —  e  (instead  of  e').  But  let  a  ponderable 
atom  be  attracted  to  the  latter  so  that  its  mass  is  thereby  so 
greatly  increased  as  to  make  the  mass  of  the  positive  particle 
vanishingly  small  in  comparison.  The  particle  —  e  may  then  be 
thought  of  as  at  rest  and  the  particle  -\-e  as  in  motion  about  the 
particle  —  e.  The  two  unlike  particles  in  the  condition  described 
constitute  then  an  Amperian  molecular  current. 

It  is  practically  this  identical  point  of  view  which  has 
been  elaborated  and  generalized  by  Lorenz  and  others 
within  the  past  decade  in  the  development  of  the  modern 
electron  theory,  with  this  single  difference,  that  we  now 
have  experimental  proof  that  it  is  the  negative  particle 
whose  mass  or  inertia  is  negligible  in  comparison  with 
that  of  the  positive  instead  of  the  reverse.  Weber  even 
went  so  far  as  to  explain  thermoelectric  and  Peltier 
effects  by  differences  in  the  kinetic  energies  in  different 
conductors  of  the  electrical  particles.1  Nevertheless  his 
explanations  are  here  widely  at  variance  with  our  modern 
conceptions  of  heat. 

Again,  in  a  paper  read  before  the  British  Association 
at  Belfast  in  1874,  G.  Johnstone  Stoney  not  only  stated 
clearly  the  atomic  theory  of  electricity,  but  actually  went 
so  far  as  to  estimate  the  value  of  the  elementary  electrical 
charge,  and  he  obtained  a  value  which  was  about  as 
reliable  as  any  which  had  been  found  until  within  quite 
recent  years.  He  got,  as  will  be  more  fully  explained  in 
the  next  chapter,  .3Xio~10  absolute  electrostatic  units, 
arid  he  got  this  result  from  the  amount  of  electricity 
necessary  to  separate  from  a  solution  one  gram  of  hydro- 
gen, combined  with  kinetic  theory  estimates  as  to  the 
number  of  atoms  of  hydrogen  in  two  grams,  i.e.,  in  one 

1  Op.  cit.t  p.  294. 


22  THE  ELECTRON 

gram  molecule  of  that  element.  This  paper  was  entitled, 
"On  the  Physical  Units  of  Nature,"  and  though  read  in 
1 8  74  it  was  not  published  in  full  until  1 88 1 .'  After  show- 
ing that  all  physical  measurements  may  be  expressed  in 
terms  of  three  fundamental  units,  he  asserts  that  it  would 
be  possible  to  replace  our  present  purely  arbitrary  units 
(the  centimeter,  the  gram,  and  the  second)  by  three 
natural  units,  namely,  the  velocity  of  light,  the  coeffi- 
cient of  gravitation,  and  the  elementary  electrical  charge. 
With  respect  to  the  last  he  says: 

Finally  nature  presents  us  with  a  single  definite  quantity  of 
electricity  which  is  independent  of  the  particular  bodies  acted  on. 
To  make  this  clear,  I  shall  express  Faraday's  law  in  the  following 
terms,  which,  as  I  shall  show,  will  give  it  precision,  viz.:  For  each 
chemical  bond  which  is  ruptured  within  an  electrolyte  a  certain 
quantity  of  electricity  traverses  the  electrolyte  which  is  the  same  in 
all  cases.  This  definite  quantity  of  electricity  I  shall  call  £,.  If 
we  make  this  our  unit  of  electricity,  we  shall  probably  have  made 
a  very  important  step  in  our  study  of  molecular  phenomena. 

Hence  we  have  very  good  reason  to  suppose  that  in  VI}  d, 
and  E2,  we  have  three  of  a  series  of  systematic  units  that  in  an 
eminent  sense  are  the  units  of  nature,  and  stand  in  an  intimate 
relation  with  the  work  which  goes  on  in  her  mighty  laboratory. 

Take  one  more  illustration  from  prominent  writers 
of  this  period.  In  his  Faraday  lecture  delivered  at  the 
Royal  Institution  in  1881,  Helmholtz  spoke  as  follows: 

Now  the  most  startling  result  of  Faraday's  law  is  perhaps  this, 
if  we  accept  the  hypothesis  that  the  elementary  substances  are 
composed  of  atoms,  we  cannot  avoid  concluding  that  electricity 
also,  positive  as  well  as  negative,  is  divided  into  definite  elementary 
portions  which  behave  like  atoms  of  electricity.2 

1  Phil.  Mag.,  XI  (1881;  sth  series),  384. 

2  Wissenschaftliche  Abhatidlungen,  III,  69. 


EARLY  VIEWS  OF  ELECTRICITY  23 

This  looks  like  a  very  direct  and  unequivocal  state- 
ment of  the  atomic  theory  of  electricity,  and  yet  in  the 
same  lecture  Helm  hoi  tz  apparently  thinks  of  metallic 
conduction  as  something  quite  different  from  electrolytic 
when  he  says: 

All  these  facts  show  that  electrolytic  conduction  is  not  at  all 
limited  to  solutions  of  acids  or  salts.  It  will,  however,  be  rather 
a  difficult  problem  to  find  out  how  far  the  electrolytic  conduction 
is  extended,  and  I  am  not  yet  prepared  to  give  a  positive  answer. 

The  context  shows  that  "he  thought  of  extending  the 
idea  of  electrolytic  conduction  to  a  great  many  insula- 
tors. But  there  is  no  indication  that  he  thought  of 
extending  it  to  metallic  conductors  and  imagining  these 
electrical  atoms  as  existing  as  discrete  individual  things 
on  charged  metals  or  as  traveling  along  a  wire  carrying  an 
electrical  current.  Nevertheless,  the  statement  quoted 
above  is  one  of  the  most  unequivocal  which  can  be  found 
anywhere  up  to  about  1899  as  to  the  atomic  nature  of 
electricity. 

The  foregoing  quotations  are  sufficient  to  show  that 
the  atonlic  theory  of  electricity,  like  the  atomic  theory 
of  matter,  is  not  at  all  new  so  far  as  the  conception  alone 
is  concerned.  In  both  cases  there  were  individuals  who 
held  almost  exactly  the  modern  point  of  view.  In  both 
cases,  too,  the  chief  new  developments  have  consisted  in 
the  appearance  of  new  and  exact  experimental  data  which 
has  silenced  criticism  and  compelled  the  abandonment 
of  other  points  of  view  which  up  to  about  1900  flourished 
along  with,  and  even  more  vigorously  than,  the  atomic 
conception.  Even  in  1897  Lord  Kelvin,  with  a  full 
knowledge  of  all  the  new  work  which  was  appearing 
on  X-rays  and  cathode  rays,  could  seriously  raise  the 


24  THE  ELECTRON 

question  whether  electricity  might  not  be  a  "  continuous 
homogeneous  liquid."     He  does  it  in  these  words: 

Varley's  fundamental  discovery  of  the  cathode  rays,  splendidly 
confirmed  and  extended  by  Crookes,  seems  to  me  to  necessitate  the 
conclusion  that  resinous  electricity,  not  vitreous,  is  The  Electric 
Fluid,  if  we  are  to  have  a  one-fluid  theory  of  electricity.  Mathe- 
matical reasons  prove  that  if  resinous  electricity  is  a  continuous 
homogeneous  liquid  it  must,  in  order  to  produce  the  phenomena 
of  contact  electricity,  which  you  have  seen  this  evening,  be 
endowed  with  a  cohesional  quality.  It  is  just  conceivable,  though 
it  does  not  at  present  seem  to  me  very  probable,  that  this  idea  may 
deserve  careful  consideration.  I  leave  it,  however,  for  the  present 
and  prefer  to  consider  an  atomic  theory  of  electricity  foreseen  as 
worthy  of  thought  by  Faraday  and  Clerk-Maxwell,  very  definitely 
proposed  by  Helmholtz  in  his  last  lecture  to  the  Royal  Institution, 
and  largely  accepted  by  present-day  workers  and  teachers.  Indeed 
Faraday's  laws  of  electrolysis  seem  to  necessitate  something  atomic 
in  electricity,  .  .  .  .* 

What  was  the  new  experimental  work  which  already 
in  1897  was  working  this  change  in  viewpoint  ?  Much 
of  it  was  at  first  little  if  at  all  more  convincing  than  that 
which  had  been  available  since  Faraday's  time.  Never- 
theless it  set  physicists  to  wondering  whether  stresses 
and  strains  in  the  ether  had  not  been  a  bit  overworked, 
and  whether  in  spite  of  their  undoubted  existence  elec- 
tricity itself  might  not  after  all  be  something  more 
definite,  more  material,  than  the  all-conquering  Maxwell 
theory  had  assumed  it  to  be. 

The  result  of  the  past  fifteen  years  has  been  to  bring 
us  back  very  close  to  where  Franklin  was  in  1750,  with 
the  single  difference  that  our  modern  electron  theory  rests 
upon  a  mass  of  very  direct  and  very  convincing  evidence, 
which  it  is  the  purpose  of  the  next  chapters  to  present. 

1  Kelvin,  "Contact  Electricity  and  Electrolysis,"  Nature,  LVI 
(1897),  84. 


CHAPTER  II 

THE  EXTENSION  OF  THE   ELECTROLYTIC  LAWS  TO 
CONDUCTION  IN  GASES 

I.      THE  ORIGIN  OF  THE  WORD  "ELECTRON" 

The  word  "electron"  was  first  suggested  in  1891  by 
Dr.  G.  Johnstone  Stoney  as  a  name  for  the  "natural  unit 
of  electricity,"  gamely,  that  quantity  of  electricity  which 
must  pass  through  a  solution  in  order  to  liberate  at  one 
of  the  electrodes  one  atom  of  hydrogen  or  one  atom  of 
any  univalent  substance.  In  a  paper  published  in  1891 
he  says: 

Attention  must  be  given  to  Faraday's  Law  of  Electrolysis, 
which  is  equivalent  to  the  statement  that  hi  electrolysis  a  definite 
quantity  of  electricity,  the  same  in  all  cases,  passes  for  each  chemi- 
cal bond  that  is  ruptured.  The  author  called  attention  to  this 
form  of  the  law  in  a  communication  made  to  the  British  Associa- 
tion in  1874  and  printed  in  the  Scientific  Proceedings  of  the  Royal 
Dublin  Society  of  February,  1881,  and  in  the  Philosophical  Maga- 
zine for  May,  1881,  pp.  385  and  386  of  the  latter.  It  is  there  shown 
that  the  amount  of  this  very  remarkable  quantity  of  electricity  is 

about  the  twentiethet  (that  is  — -)  of  the  usual  electromagnetic 
unit  of  electricity,  i.e.,  the  unit  of  the  Ohm  series.  This  is  the 
same  as  3  eleventhets  ( — -  )  of  the  much  smaller  C.G.S.  electro- 
static unit  of  quantity.  A  charge  of  this  amount  is  associated  in 
the  chemical  atom  with  each  bond.  There  may  accordingly  be 
several  such  charges  in  one  chemical  atom,  and  there  appear  to  be 
at  least  two  in  each  atom.  These  charges,  which  it  will  be  con- 
venient to  call  "electrons,"  cannot  be  removed  from  the  atom, 
but  they  become  disguised  when  atoms  chemically  unite.  If  an 

25 


26  THE  ELECTRON 

electron  be  lodged  at  the  point  P  of  the  molecule  which  undergoes 
the  motion  described  in  the  last  chapter,  the  revolution  of  this 
charge  will  cause  an  electromagnetic  undulation  in  the  surrounding 
ether.1 

It  will  be  noticed  from  this  quotation  that  the  word 
"  electron"  was  introduced  to  denote  simply  a  definite  ele- 
mentary quantity  of  electricity  without  any  reference  to 
the  mass  or  inertia  which  may  be  associated  with  it,  and 
Professor  Stoney  implies  that  every  atom  must  contain 
at  least  two  electrons,  one  positive  and  one  negative, 
because  otherwise  it  would  be  impossible  that  the  atom 
as  a  whole  be  electrically  neutral.  As  a  matter  of  fact 
the  evidence  is  now  considerable  that  the  hydrogen 
atom  does  indeed  contain  just  one  positive  and  one 
negative  electron. 

It  is  unfortunate  that  modern  writers  have  not  been 
more  careful  to  retain  the  original  significance  of  the  word 
introduced  by  Professor  Stoney,  for  it  is  obvious  that  a 
word  is  needed  which  denotes  merely  the  elementary  unit 
of  electricity  and  has  no  implication  as  to  where  that 
unit  is  found,  to  what  it  is  attached,  with  what  inertia 
it  is  associated,  or  whether  it  is  positive  or  negative  in 
sign;  and  it  is  also  apparent  that  the  word  "  electron" 
is  the  logical  one  to  associate  with  this  conception.2 

1  Scientific  Transactions  of  the  Royal  Dublin  Society,  IV  (1891;  ntl, 
series),  563. 

2  The  most  authoritative  writers,  Thomson,  Rutherford,  Campbell, 
Richardson,  etc.,  have  in  fact  retained  the  original  significance  of  the 
word  "electron"  instead  of  using  it  to  denote  solely  the  free  negative 

electron  or  corpuscle  of  J.  J.  Thomson,  the  mass  of  which  is  -    -  of 


that  of  the  hydrogen  atom.  All  of  these  writers  in  books  or  articles 
written  since  1913  have  treated  of  positive  as  well  as  negative  electrons, 
although  the  mass  associated  with  the  former  is  never  less  than  that  of 
the  hydrogen  atom. 


CONDUCTION  IN  GASES  27 

J.  J.  Thomson's  word  "  corpuscle  "  is  a  very  appropriate 
one  to  denote  the  very  minute  inertia  with  which  the 
negative  electron  is  found  associated  in  cathode  rays. 

e 

II.      THE  DETERMINATION  OF  —  AND  N€  FROM  THE  FACTS 

m 

OF   ELECTROLYSIS 

Faraday's  experiments  had  of  course  not  furnished 
the  data  for  determining  anything  about  how  much  elec- 
tricity an  electron  represents  in  terms  of  the  standard 
unit  by  which  electrical  charges  are  ordinarily  measured 
in  the  laboratory.  This  is  called  the  coulomb,  and 
represents  the  quantity  of  electricity  conveyed  in 
one  second  by  one  ampere.  Faraday  had  merely  shown 
that  a  given  current  flowing  in  succession  through 
solutions  containing  different  univalent  elements  like 
hydrogen  or  silver  or  sodium  or  potassium  would  deposit 
weights  of  these  substances  which  are  exactly  propor- 
tional to  their  respective  atomic  weights.  This  enabled 
him  to  assert  that  one  and  the  same  amount  of  elec- 
tricity is  associated  in  the  process  of  electrolysis  with 
an  atom  of  each  of  these  substances.  He  thought  of  this 
charge  as  carried  by  the  atom,  or  in  some  cases  by  a  group 
of  atoms,  and  called  the  group  with  its  charge  an  "ion," 
that  is,  a  "goer,"  or  "traveler."  Just  how  the  atoms 
come  to  be  charged  in  a  solution  Faraday  did  not  know, 
nor  do  we  know  now  with  any  certainty.  Further,  we 
do  not  know  how  much  of  the  solvent  an  ion  associates 
with  itself  and  drags  with  it  through  the  solution.  But 
we  do  know  that  when  a  substance  like  salt  is  dissolved 
in  water  many  of  the  neutral  NaCl  molecules  are  split 
up  by  some  action  of  the  water  into  positively  charged 


28  THE  ELECTRON 

sodium  (Na)  ions  and  negatively  charged  chlorine  (Cl) 
ions.  The  ions  of  opposite  sign  doubtless  are  all  the 
time  recombining,  but  others  are  probably  continually 
forming,  so  that  at  each  instant  there  are  many  uncom- 
bined  ions.  Again,  we  know  that  when  a  water  solution 
of  copper  sulphate  is  formed  many  of  the  neutral  CuSO4 
molecules  are  split  up  into  positively  charged  Cu  ions 
and  negatively  charged  S04  ions.  In  this  last  case  too 
we  find  that  the  same  current  which  will  deposit  in  a 
given  time  from  a  silver  solution  a  weight  of  silver  eqnn1 
to  its  atomic  weight  will  deposit  from  the  copper-sulpha i 
solution  in  the  same  time  a  weight  of  copper  equal  t< 
exactly  one-half  its  atomic  weight.  Hence  we  know  that 
the  copper  ion  carries  in  solution  twice  as  much  elec- 
tricity as  does  the  silver  ion,  that  is,  it  carries  a  charge  of 
two  electrons. 

But  though  we  could  get  from  Faraday's  experiments 
no  knowledge  about  the  quantity  of  electricity,  e,  repre- 
sented by  one  electron,  we  could  get  very  exact  informa- 
tion about  the  ratio  of  the  ionic  charge  E  to  the  mass 
of  the  atom  with  which  it  is  associated  in  a  given  solution. 

For,  if  the  whole  current  which  passes  through  a 
solution  is  carried  by  the  ions — and  if  it  were  not  we 
should  not  always  find  the  deposits  exactly  proportional 
to  atomic  weights — then  the  ratio  of  the  total  quantity 
of  electricity  passing  to  the  weight  of  the  deposit  pro- 
duced must  be  the  same  as  the  ratio  of  the  charge  E  on 
each  ion  to  the  mass  m  of  that  .ion.  But  by  international 
agreement  one  absolute  unit  of  electricity  has  been 
defined  in  the  electromagnetic  system  of  units  as  the 
amount  of  electricity  which  will  deposit  from  a  silver 
solution  o.oiiiS  grams  of  metallic  silver.  Hence  if  m 


CONDUCTION  IN  GASES  29 

refers  to  the  silver  ion  and  E  means  the  charge  on  the 
ion,  we  have 

for  silver  —  =  —     —  -  =80.44  electromagnetic  units  ; 
m    0.01118 

or  if  m  refers  to  the  hydrogen  ion,  since  the  atomic 

weight  of  silver  is  -  -  -  times  that  of  hydrogen, 
i.ooo 

E          i       ,,107.88 
for  hydrogen  -=——--     =  9,573, 


which  is  about  io4  electromagnetic  units. 

7^ 
Thus  in  electrolysis  —  varies  from  ion  to  ion,  being 

for  univalent  ions,  for  which  E  is  the  same  and  equal  to 
one  electron  e,  inversely  proportional  to  the  atomic 
weight  of  the  ion.  For  polivalent  ions  E  may  be  2,  3, 
4,  or  5  electrons,  but  since  hydrogen  is  at  least  7  times 
lighter  than  any  other  ion  which  is  ever  found  in  solution, 

and  its  charge  is  but  one  electron,  we  see  that  the  largest 
17 

value  which  —  ever  has  in  electrolysis  is  its  value  for 
m 

hydrogen,  namely,  about  io4  electromagnetic  units. 

Ei 

Although  —  varies  with  the  nature  of  the  ion,  there  is 

a  quantity  which  can  be  deduced  from  it  which  is  a  uni- 
versal constant.  This  quantity  is  denoted  by  Ne,  where 
e  means  as  before  an  electron  and  N  is  the  Avogadro  con- 
stant or  the  number  of  molecules  in  r6  grams  of  oxygen, 
i.e.,  in  one  gram  molecule.  We  can  get  this  at  once  from 

7^ 

the  value  of  --  by  letting  m  refer  to  the  mass  of  that 

m    J 

imaginary   univalent   atom  which   is  the   unit   of    our 


30  THE  ELECTRON 

atomic  weight  system,  namely,  an  atom  which  is  exactly 
1/16  as  heavy  as  oxygen  or  1/107.88  as  heavy  as  silver. 
For  such  an  atom 

E_e  _  107.88  _ 

m    m    0.01118     9'  5 

Multiplying  both  numerator  and  denominator  by  N  and 
remembering  that  for  this  gas  one  gram  molecule  means 
•i  gram,  that  is,  Nm=  i,  we  have 

^=9650  absolute  electromagnetic  units, (i) 

and  since  the  electromagnetic  unit  is  equivalent  to 
3Xio10  electrostatic  units,  we  have 

7Ve=28,95oXio10  absolute  electrostatic  units. 

Further,  since  a  gram  molecule  of  an  ideal  gas  under 
standard  conditions,  i.e.,  at  o°  C.  76  cm.  pressure, 
occupies  22412  c.c.,  if  wx  represents  the  number  of  mole- 
cules of  such  a  gas  per  cubic  centimeter  at  o°  C.,  76  cm., 
we  have 

nrf  =  — — =i  .202Xio10  electrostatic  units. 

22,412 

Or  if  n  represent  the  number  of  molecules  per  cubic 
centimeter  at  15°  C.  76  cm.,  we  should  have  to  multiply 
the  last  number  by  the  ratio  of  absolute  temperatures, 
i.e.,  by  273/288  and  should  obtain  then. 

ne=i . 225X10™ (2) 

Thus,  even  though  the  facts  of  electrolysis  give  us  no 
information  at  all  as  to  how  much  of  a  charge  one  electron 
e  represents,  they  do  tell  us  very  exactly  that  if  we  should 
take  e  as  many  times  as  there  are  molecules  in  a  gram 


CONDUCTION  IN  GASES  31 

molecule  we  should  get  exactly  9,650  absolute  electro- 
magnetic units  of  electricity.  This  is  the  amount  of 
electricity  conveyed  by  a  current  of  i  ampere  in  10  sec- 
onds. Until  quite  recently  we  have  been  able  to  make 
nothing  better  than  rough  guesses  as  to  the  number  of 
molecules  in  a  gram  molecule,  but  with  the  aid  of  these 
guesses,  obtained  from  the  Kinetic  Theory,  we  have,  of 
course,  been  enabled  by  (i)  to  make  equally  good 
guesses  about  e.  These  guesses,  based  for  the  most  part 
on  quite  uncertain  computations  as  to  the  average  radius 
of  a  molecule  of  air,  placed  N  anywhere  between  2X  io2 
and  2oXio23.  It  was  in  this  way  that  G.  Johnstone 
Stoney  in  1874  estimated  e  at  .3Xio~10  E.S.  units.  In 
O.  E.  Meyer's  Kinetische  Theorie  der  Gase  (p.  335;  1899), 
n,  the  number  of  molecules  in  a  cubic  centimeter  is  given 
as  6X  io19.  This  would  correspond  to  e=  2X  io~10.  In 
all  this  e  is  the  charge  carried  by  a  univalent  ion  in  solu- 
tion and  N  or  n  is  a  pure  number,  which  is  a  characteristic 
gas  constant,  it  is  true,  but  the  analysis  has  nothing  what- 
ever to  do  with  gas  conduction. 

III.      THE  NATURE   OF  GASEOUS  CONDUCTION 

The  question  whether  gases  conduct  at  all,  and  if  so, 
whether  their  conduction  is  electrolytic  or  metallic  or 
neither,  was  scarcely  attacked  until  about  1895.  Cou- 
lomb in  1785  had  concluded  that  after  allowing  for  the 
leakage  of  the  supports  of  an  electrically  charged  con- 
ductor, some  leakage  must  be  attributed  to  the  air  itself, 
and  he  explained  this  leakage  by  assuming  that  the  air 
molecules  became  charged  by  contact  and  were-  then 
repelled — a  wholly  untenable  conclusion,  since,  were  it 
true,  no  conductor  in  air  could  hold  a  charge  long  even 


32  THE  ELECTRON 

at  low  potentials,  nor  could  a  very  highly  charged  con- 
ductor lose  its  charge  very  rapidly  when  charged  above 
a  certain  potential  and  then  when  the  potential  fell  below 
a  certain  critical  value  cease  almost  entirely  to  lose  it. 
This  is  what  actually  occurs.  Despite  the  erroneousness 
of  this  idea,  it  persisted  in  textbooks  written  as  late  as 
1900. 

Warburg  in  1872  experimented  anew  on  air  leakage 
and  was  inclined  to  attribute  it  all  to  dust  particles.  The 
real  explanation  of  gas  conduction  was  not  found  until 
after  the  discovery  of  X-rays  in  1895.  The  convincing 
experiments  were  made  by  J.  J.  Thomson,  or  at  his 
instigation  in  the  Cavendish  Laboratory  at  Cambridge, 
England.  The  new  work  grew  obviously  and  simply  out 
of.  the  fact  that  X-rays,  and  a  year  or  two  later  radium 
rays,  were  found  to  discharge  an  electroscope,  i.e.,  to 
produce  conductivity  in  a  gas.  Theretofore  no  agencies 
had  been  known  by  which  the  electrical  conductivity  of 
a  gas  could  be  controlled  at  will.  Thomson  and  his 
pupils  found  that  the  conductivity  induced  in  gases 
by  X-rays  disappeared  when  the  gas  was  sucked 
through  glass  wool.1  It  was  also  found  to  be  reduced 
when  the  air  was  drawn  through  narrow  metal  tubes. 
Furthermore,  it  was  removed  entirely  by  passing  the 
stream  of  conducting  gas  between  plates  which  were 
maintained  at  a  sufficiently  large  potential  difference. 
The  first  two  experiments  showed  that  the  conduc- 
tivity was  due  to  something  which  could  be  removed 
from  the  gas  by  filtration,  or  by  diffusion  to  the  walls  of 
a  metal  tube;  the  last  proved  that  this  something  was 
electrically  charged. 

1  J.  J.  Thomson  and  E.  Rutherford,  Phil.  Mag.,  XLII  (1896),  392. 


CONDUCTION  IN  GASES  33 

When  it  was  found,  further,  that  the  electric  cur- 
rent obtained  from  air  existing  between  two  plates 
and  traversed  by  X-rays,  rose  to  a  maximum  as 
the  P.D.  between  the  plates  increased,  and  then 
reached  a  value  which  was  thereafter  independent  of  this 
potential  difference;  and,  further,  that  this  conductivity 
of  the  air  died  out  slowly  through  a  period  of  several 
seconds  when  the  X-ray  no  longer  acted,  it  was  evident 
that  the  qualitative  proof  was  complete  that  gas  con- 
duction must  be  due  to  charged  particles  produced  in  the 
air  at  a  definite  rate  by  a  constant  source  of  X-rays,  and 
that  these  charged  particles,  evidently  of  both  plus  and 
minus  signs,  disappear  by  recombination  when  the  rays 
are  removed.  The  maximum  or  saturation  currents 
which  could  be  obtained  when  a  given  source  was  ionizing 
the  air  between  two  plates  whose  potential  difference 
could  be  varied  was  obviously  due  to  the  fact  that  when 
the  electric  field  between  the  plates  became  strong  enough 
to  sweep  all  the  ions  to  the  plates  as  fast  as  they  were 
formed,  none  of  them  being  lost  by  diffusion  or  recom- 
bination, the  current  obtained  could,  of  course,  not  be 
increased  by  further  increase  in  the  field  strength.  Thus 
gas  conduction  was  definitely  shown  about  1896  to  be 
electrolytic  in  nature. 

IV.      COMPARISON  OF  THE  GASEOUS  ION  AND  THE 
ELECTROLYTIC  ION 

But  what  sort  of  ions  were  these  that  were  thus 
formed?  We  did  not  know  the  absolute  value  of  the 
charge  on  a  univalent  ion  in  electrolysis,  but  we  did 
know  accurately  ne.  Could  this  be  found  for  the  ions 
taking  part  in  gas  conduction  ?  That  this  question  was 


34  THE  ELECTRON 

answered  affirmatively  was  due  to  the  extraordinary 
insight  and  resourcefulness  of  J.  J.  Thomson  and  his 
pupils  at  the  Cavendish  Laboratory  in  Cambridge,  both 
in  working  out  new  theoretical  relations  and  in  devising 
new  methods  for  attacking  the  new  problems  of  gaseous 
conduction.  These  workers  found  first  a  method  of 
expressing  the  quantity  ne  in  terms  of  two  measurable 
constants,  called  (i)  the  mobility  of  gaseous  ions  and 
(2)  the  coefficient  of  diffusion  of  these  ions.  Secondly, 
they  devised  new  methods  of  measuring  these  two 
constants — constants  which  had  never  before  been  deter- 
mined. The  theory  of  the  relation  between  these  con- 
stants and  the  quantity  ne  will  be  found  in  Appendix  A. 
The  result  is 

ne^P,  (3) 

in  which  P  is  the  pressure  existing  in  the  gas  and  v0  and 
D  are  the  mobility  and  the  diffusion  coefficients  respec- 
tively of  the  ions  at  this  pressure. 

If  then  we  can  find  a  way  of  measuring  the  mobilities 
v0  of  atmospheric  ions  and  also  the  diffusion  coefficients 
D,  we  can  find  the  quantity  ne,  in  which  n  is  a  mere  num- 
ber, viz.,  the  number  of  molecules  of  air  per  cubic  centi- 
meter at  15°  C.,  76  cm.  pressure,  and  e  is  the  average 
charge  on  an  atmosphere  ion.  We  shall  then  be  in  posi- 
tion to  compare  this  with  the  product  we  found  in  (2)  on 
p.  30,  in  which  n  had  precisely  the  same  significance  as 
here,  but  e  meant  the  average  charge  carried  by  a  uni- 
valent  ion  in  electrolysis. 

The  methods  devised  in  the  Cavendish  Laboratory 
between  1897  and  1903  for  measuring  the  mobilities  and 
the  diffusion  coefficients  of  gaseous  ions  have  been  used 


CONDUCTION  IN  GASES  35 

in  all  later  work  upon  these  constants.  The  mobilities 
were  first  determined  by  Rutherford  in  1897,*  then  more 
accurately  by  another  method  in  i8c}8.2  Zeleny  devised 
a  quite  distinct  method  in  igoo,3  and  Langevin  still 
another  method  in  1 903.4  These  observers  all  agree 
closely  in  finding  the  average  mobility  (velocity  in  unit 
field)  of  the  negative  ion  in  dry  air  about  i .  83  cm.  per 
second,  while  that  of  the  positive  ion  was  found  but 
1.35  cm.  per  second.  In  hydrogen  these  mobilities  were 
about  7.8  cm.  per  second  and  6.1  cm.  per  second, 
respectively,  and  in  general  the  mobilities  in  different 
gases,  though  not  in  vapors,  seem  to  be  roughly  in  the 
inverse  ratio  of  the  square  roots  of  the  molecular  weights. 
The  diffusion  coefficients  of  ions  were  first  measured 
in  1900  by  Townsend,  now  professor  of  physics  in  Oxford, 
England,5  by  a  method  devised  by  him  and  since  then 
used  by  other  observers  in  such  measurements.  If  we 
denote  the  diffusion  coefficient  of  the  positive  ion  by  D+ 
and  that  of  the  negative  by  D— ,  Townsend's  results  in 
dry  air  may  be  stated  thus: 

#+  =  0.028 

D-  =0.043. 

These  results  are  interesting  in  two  respects.  In  the 
first  place,  they  seem  to  show  that  for  some  reason  the 
positive  ion  in  air  is  more  sluggish  than  the  negative, 
since  it  travels  but  about  0.7  (=1.35/1.81)  as  fast  in  a 
given  electrical  field  and  since  it  diffuses  through  air  but 
about  0.7  (=28/43)  as  rapidly.  In  the  second  place, 

'  Phil,  Mag.,  XLIV  (1898),  422. 

3  Proc.  Camb.  Phil.  Soc.,  IX,  401. 
*  Phil.  Trans.,  A  195,  p.  193. 

4  Annale  de  Chimie  el  de  Physique,  XXVIII,  289. 

5  Phil,  Trans.,  A  193,  p.  129. 


36  THE  ELECTRON 

the  results  of  Townsend  show  that  an  ion  is  very  much 
more  sluggish  than  is  a  molecule  of  air,  for  the  coefficient 
of  diffusion  of  oxygen  through  air  is  0.178,  which  is  four 
times  the  rate  of  diffusion  of  the  negative  ion  through 
air  and  five  times  that  of  the  positive  ion.  This  sluggish- 
ness of  ions  as  compared  with  molecules  was  at  first  uni- 
versally considered  to  mean  that  the  gaseous  ion  is  not 
a  single  molecule  with  an  attached  electrical  charge,  but 
a  cluster  of  perhaps  from  three  to  twenty  molecules  held 
together  by  such  a  charge.  If  this  is  the  correct  inter- 
pretation, then  for  some  reason  the  positive  ion  in  air 
is  a  larger  cluster  than  is  the  negative  ion. 

It  has  been  since  shown  by  a  number  of  observers 
that  the  ratio  of  the  mobilities  of  the  positive  and  nega- 
tive ions  is  not  at  all  the  same  in  other  gases  as  it  is  in 
air.  In  carbon  dioxide  the  two  mobilities  have  very 
nearly  the  same  value,  while  in  chlorine,  water  vapor,  and 
the  vapor  of  alcohol  the  positive  ion  apparently  has  a 
slightly  larger  mobility  than  the  negative.  There  seems 
to  be  some  evidence  that  the  negative  ion  has  the  larger 
mobility  in  gases  which  are  electro- positive,  while  the 
positive  has  the  larger  mobility  in  the  gases  which 
are  strongly  electro-negative.  This  dependence  of  the 
ratio  of  mobilities  upon  the  electro-positive  or  electro- 
negative character  of  the  gas  has  usually  been  considered 
strong  evidence  in  favor  of  the  cluster-ion  theory. 

Very  recently,  however,  Loeb,1  who  has  worked  at  the 
Ryerson  Laboratory  on  mobilities  in  powerful  electric 
fields,  and  Wellish,2  who,  at  Yale,  has  measured  mobilities 

1  Leonard  B.  Loeb,  Proc,  Nat.  Acad.,  II  (1916),  345,  and  Phys. 
Rev.,  1917. 

*  Wellish,  Am.  Jour,  of  Science,  XXXIX  (1915),  583. 


CONDUCTION  IN  GASES  37 

at  very  low  pressures,  have  concluded  that  their  results 
are  not  consistent  with  the  cluster-ion  theory,  but  must 
rather  be  interpreted  in  terms  of  the  so-called  Atom-ion 
Theory.  This  theory  seeks  to  explain  the  relative 
sluggishness  of  ions,  as  compared  with  molecules,  by 
the  additional  resistance  which  the  gaseous  medium 
offers  to  the  motion  of  a  molecule  through  it  when  that 
molecule  is  electrically  charged.  According  to  this  hypoth- 
esis, the  ion  would  be  simply  an  electrically  charged 
molecule. 

Fortunately,  the  quantitative  evidence  for  the  elec- 
trolytic nature  of  gas  conduction  is  in  no  way  dependent 
upon  the  correctness  of  either  one  of  the  theories  as  to 
the  nature  of  the  ion.  It  depends  simply  upon  the  com- 
parison of  the  values  of  ne  obtained  from  electrolytic 
measurements,  and  those  obtained  from  the  substitution 
in  equation  3  of  the  measured  values  of  v0  and  D  for 
gaseous  ions. 

As  for  these  measurements,  results  obtained  by 
Franck  and  Westphal,1  who  in  1908  repeated  in  Berlin 
both  measurements  on  diffusion  coefficients  and  mobility 
coefficients,  agree  within  4  or  5  per  cent  with  the  results 
published  by  Townsend  in  1900.  According  to  both  of 
these  observers,  the  value  of  ne  for  the  negative  ions  pro- 
duced in  gases  by  X-rays,  radium  rays,  and  ultra-violet 
light  came  out,  within  the  limits  of  experimental  error, 
which  were  presumably  5  or  6  per  cent,  the  same  as  the 
value  found  for  univalent  ions  in  solutions,  namely, 
i.  23X10™  absolute  electrostatic  units.  This  result 
seems  to  show  with  considerable  certainty  that  the 
negative  ions  in  gases  ionized  by  X-rays  or  similar 

1  Verh.  der  deutsch.  phys.  Ges.,  XI  (1909),  146  and  276. 


38  THE  ELECTRON 

agencies  carry  on  the  average  the  same  charge  as  that 
borne  by  the  univalent  ion  in  electrolysis.  When  we 
consider  the  work  on  the  positive  ion,  our  confidence  in 
the  inevitableness  of  the  conclusions  reached  by  the 
methods  under  consideration  is  perhaps  somewhat 
shaken.  For  Townsend  found  that  the  value  of  ne  for 
the  positive  ion  came  out  about  14  per  cent  higher  than 
the  value  of  this  quantity  for  the  univalent  ion  in  elec- 
trolysis, a  result  which  he  does  not  seem  at  first  to  have 
regarded  as  inexplicable  on  the  basis  of  experimental 
uncertainties  in  his  method.  In  1908,  however,1  he 
devised  a  second  method  of  measuring  the  ratio  of  the 
mobility  and  the  diffusion  coefficient  and  obtained  this 
time,  as  before,  for  the  negative  ion,  ne—  i .  23 X  io10,  but 
for  the  positive  ion  twice  that  amount,  namely,  2 . 46 X  io10. 
From  these  last  experiments  he  concluded  that  the 
positive  ions  in  gases  ionized  by  X-rays  carried  on  the 
average  twice  the  charge  carried  by  the  univalent  ion  in 
electrolysis.  Franck  and  Westphal,  however,  found  in 
their  work  that  Townsend's  original  value  for  ne  for  the 
positive  ions  was  about  right,  and  hence  concluded  that 
only  about  9  per  cent  of  the  positive  ions  could  carry  a 
charge  of  value  ie.  Work  which  will  be  described  later 
indicates  that  neither  Townsend's  nor  Franck  and  West- 
phal's  conclusions  are  correct,  and  hence  point  to  errors 
of  some  sort  in  both  methods.  But  despite  these  diffi- 
culties with  the  work  on  positive  ions,  it  is  nevertheless 
fair  to  say  that  Townsend  was  the  first  to  bring  forward 
strong  quantitative  evidence  that  the  mean  charge 
carried  by  the  negative  ions  in  ionized  gases  is  the  same 
as  the  mean  charge  carried  by  univalent  ions  in  solu- 
1  Proc.  Roy.  Soo.,  LXXX  (1908),  207. 


CONDUCTION  IN  GASES  39 

tions,  and  that  the  mean  charge  carried  by  the  positive 
ions  in  gases  has  not  far  from  the  same  value. 

But  there  is  one  other  advance  of  fundamental  impor- 
tance which  came  with  the  study  of  the  properties  of 
gases  ionized  by  X-rays.  For  up  to  this  time  the  only 
type  of  ionization  known  was  that  observed  in  solution 
and  here  it  is  always  some  compound  molecule  like 
sodium  chloride  (NaCl)  which  splits  up  spontaneously 
into  a  positively  charged  sodium  ion  and  a  negatively 
charged  chlorine  ion.  But  the  ionization  produced  in 
gases  by  X-rays  was  of  a  wholly  different  sort,  for  it  was 
observable  in  pure  gases  like  nitrogen  or  oxygen,  or  even 
in  monatomic  gases  like  argon  and  helium.  Plainly  then 
the  neutral  atom  even  of  a  monatomic  substance  must 
possess  minute  electrical  charges  as  constituents.  Here 
we  had  the  first  direct  evidence  (i)  that  an  atom  is  a 
complex  structure,  and  (2)  that  electrical  charges  enter 
into  its  make-up.  With  this  discovery,  due  directly  to  the 
use  of  the  new  agency,  X-rays,  the  atom  as  an  ultimate, 
indivisible  thing  was  gone,  and  the  era  of  the  study  of  the 
constituents  of  the  atom  began.  And  with  astonishing 
rapidity  during  the  past  twenty  years  the  properties  of 
the  subatomic  world  have  been  revealed. 

Physicists  began  at  once  to  seek  diligently  and  to  find 
at  least  partial  answers  to  questions  like  these: 

1.  What  are  the  masses  of  the  constituents  .of  the 
atoms  torn  asunder  by  X-rays  and  similar  agencies  ? 

2.  What  are  the  values  of  the  charges  carried  by 
these  constituents  ? 

3.  How  many  of  these  constituents  are  there? 

4.  How  large  are  they,  i.e.,  what  volumes  do  they 
occupy  ? 


40  THE  ELECTRON 

5.  What  are   their   relations   to   the   emission   and 
absorption  of  light  and  heat  waves,  i.e.,  of  electromag- 
netic radiation  ? 

6.  Do  all  atoms  possess  similar  constituents?     In 
other  words,  is  there  a  primordial  subatom  out  of  which 
atoms  are  made  ? 

The  partial  answer  to  the  first  of  these  questions  came 
with  the  study  of  the  electrical  behavior  of  rarefied  gases 
in  so-called  vacuum  tubes.     J.  J.  Thomson1  and  Wie 
chert2  showed  independently  in  1897  that  the  value  of 

p 

-  for  the  negative  ion  in  such  exhausted  tubes  is  about 
m 

i.SXio7  electromagnetic  units,  or  about  1,800  times  the 

o 

value  of  —  for  the  hydrogen  ion  in  solutions.     Since  the 

approximate  equality  of  ne  in  gases  and  solutions  meant 
that  e  was  at  least  of  the  same  order  in  both,  the  only 
possible  conclusion  was  that  the  negative  ion  which 
appears  in  discharges  in  exhausted  tubes  has  a  mass,  i.e., 
an  inertia  only  i/i,8ooth  of  the  mass  of  the  lightest 
known  atom,  namely,  the  atom  of  hydrogen. 

Furthermore,   these  and  other  experimenters  have 

shown  that  —  for  the  negative  carrier  is  always  the  same 

whatever  be  the  nature  of  the  residual  gas  in  the  dis- 
charge tube.  This  was  an  indication  of  an  affirmative 
answer  to  the  sixth  question  above — an  indication  which 
was  strengthened  by  Zeeman's  discovery  in  1897  of  the 
splitting  by  a  magnetic  field  of  a  single  spectral  line  into 
two  or  three  lines;  for  this,  when  worked  out  quantita- 

'  Phil.  Mag.,  XLIV  (1897),  298. 

*  Verh.  der  phys.-okon.  Ges.  zu  Konigsberg,  1897. 


CONDUCTION  IN  GASES  41 

lively,  pointed  to  the  existence  within  the  atom  of  a 
negatively  charged  particle  which  had  approximately  the 

same  value  of  — . 
m 

The  study  of  —  for  the  positive  ions  in  exhausted  tubes, 
m 

though  first  carried  out  quantitatively  by  Wien,1  has  been 
most  elaborately  and  most  successfully  dealt  with  by 
J.  J.  Thomson.2  The  results  of  the  work'  of  all  observers 

up  to  date  seem  to  show  quite  conclusively  that  —  for  a 

positive  ion  in  gases  is  never  larger  than  its  value  for  the 
hydrogen  ion  in  electrolysis,  and  that  it  varies  with 
different  sorts  of  residual  gases  just  as  it  is  found  to  do 
in  electrolysis. 

In  a  word,  then,  the  act  of  ionization  in  gases  appears 
to  consist  in  the  detachment  from  a  neutral  atom  of  one 
or  more  negatively  charged  particles,  called  by  Thomson 
corpuscles.  The  residuum  of  the  atom  is  of  course  posi- 
tively charged,  and  it  always  carries  practically  the 
whole  mass  of  the  original  atom.  The  detached  cor- 
puscle must  soon  attach  itself,  in  a  gas  at  ordinary  pres- 
sure, to  a  neutral  atom,  since  otherwise  we  could  not 
account  for  the  fact  that  the  mobilities  and  the  diffusion 
coefficients  of  negative  ions  are  usually  of  the  same  order 
of  magnitude  as  those  of  the  positive  ions.  It  is  because 
of  this  tendency  of  the  parts  of  the  dissociated  atom  to 
form  new  attachments  in  gases  at  ordinary  pressure  that 
the  inertias  of  these  parts  had  to  be  worked  out  in  the 
rarefied  gases  of  exhausted  tubes. 

1  W.  Wien,  Wied.  Ann.,  LXV  (1898),  440. 

2  Rays  of  Positive  Electricity,  London:  Longmans,  1913. 


42  THE  ELECTRON 

The  foregoing  conclusions  as  to  the  masses  of  the 
positive  and  negative  constituents  of  atoms  had  all  been 
reached  before  1900,  mostly  by  the  workers  in  the 
Cavendish  Laboratory,  and  subsequent  investigation  has 
not  modified  them  in  any  essential  particulars. 

The  history  of  the  development  of  our  present  knowl- 
edge of  the  charges  carried  by  the  constituents  will  be 
detailed  in  the  next  chapters. 


CHAPTER  III 

EARLY  ATTEMPTS  AT  THE  DIRECT  DETER- 
MINATION OF  e 

Although  the  methods  sketched  in  the  preceding 
chapters  had  been  sufficient  to  show  that  the  mean 
charges  carried  by  ions  in  gases  are  the  same  or  nearly 
the  same  as  the  mean  charges  carried  by  univalent  ions 
in  solution,  in  neither  case  had  we  any  way  of  determin- 
ing what  the  absolute  value  of  that  mean  charge  is,  nor, 
indeed,  had  we  any  proof  even  that  all  the  ions  of  a  given 
kind,  e.g.,  silver  or  hydrogen,  carry  the  same  charge.  Of 
course,  the  absolute  value  of  e  could  be  found  from  the 
measured  value  of  ne  if  only  n,  the  number  of  molecules 
in  i  c.c.  of  gas  under  standard  conditions,  were  known. 
But  we  had  only  rough  guesses  as  to  this  number.  These 
guesses  varied  tenfold,  and  none  of  them  were  based 
upon  considerations  of  recognized  accuracy  or  even 
validity. 

i.    TOWNSEND'S  WORK  ON  e 

The  first  attempt  at  a  direct  determination  of  e  was 
published  by  Townsend  in  a  paper  read  before  the 
Cambridge  Philosophical  Society  on  February  8,  1897. x 
Townsend's  method  was  one  of  much  novelty  and  of  no 
little  ingenuity.  It  is  also  of  great  interest  because  it 
contains  all  the  essential  elements-  of  some  of  the  sub- 
sequent determinations. 

1  Proceedings,  IX  (1897),  244. 

43 


44  THE  ELECTRON 

It  had  been  known,  even  to  Laplace  and  Lavoisier  a 
hundred  years  before,  that  the  hydrogen  gas  evolved 
when  a  metal  dissolves  in  an  acid  carries  with  it  an  elec- 
trical charge.  This  " natural  method''  of  obtaining  a 
charge  on  a  gas  was  scarcely  studied  at  all,  however, 
until  after  the  impulse  to  the  study  of  the  electrical 
properties  of  gases  had  been  given  by  the  discovery  in 
1896  that  electrical  properties  can  be  artificially  imparted 
to  gases  by  X-rays.  Townsend's  paper  appeared  within 
a  year  of  that  time.  Enright1  had  indeed  found  that- 
the  hydrogen  given  off  when  iron  is  dissolving  in  sul- 
phuric acid  carries  with  it  a  positive  charge,  but  Oliver 
Lodge2  had  urged  that  it  was  not  the  gas  itself  which 
carries  the  charge  but  merely  the  spray,  for  the  frictional 
electrification  of  spray  was  a  well-known  phenomenon. 
Indeed,  it  has  always  been  assumed  that  the  gas  mole- 
cules which  rise  from  the  electrodes  in  electrolysis  are 
themselves  neutral.  Townsend,  however,  first  showed 
that  some  of  these  molecules  are  charged,  although  there 
are  indeed  a  million  million  neutral  ones  for  every  one 
carrying  a  charge.  He  found  that  both  the  oxygen  and 
the  hydrogen  which  appear  at  the  opposite  electrodes 
when  sulphuric  acid  is  electrolyzed  are  positively  charged, 
while  when  the  electrolyte  is  caustic  potash  both  the  oxy- 
gen and  the  hydrogen  given  off  are  negative.  Townsend's 
electrolyzing  currents  were  from  12  to  14  amperes.  He 
got  in  this  way  many  more  ions  per  cubic  centimeter 
than  he  could  produce  with  X-rays,  the  total  charge 
per  cubic  centimeter  being  as  large  as  5Xio~3  electro- 
static units. 

1  Phil.  Mag.,  XXIX  (1890;   sth  series),  56. 

2  Ibid.,  292;  Nature,  XXXVI,  412. 


EARLY  DETERMINATIONS  OF  e  45 

When  these  charged  gases  were  bubbled  through 
water  they  formed  a  cloud.  This  cloud  could  be  com- 
pletely removed  by  bubbling  through  concentrated  sul- 
phuric acid  or  any  drying  agent,  but  when  the  gas  came 
out  again  into  the  atmosphere  of  the  room  it  again  con- 
densed moisture  and  formed  a  stable  cloud.  Townsend 
says  that  "the  process  of  forming  the  cloud  in  positive 
or  negative  oxygen  by  bubbling  through  water,  and 
removing  it  again  by  bubbling  through  sulphuric  acid, 
can  be  gone  through  without  losing  more  than  20  or  25 
per  cent  of  the  original  charge  on  the  gas."  This  means 
simply  that  the  ions  condense  the  water  about  them 
when  there  is  an  abundance  of  moisture  in  the  air,  but 
when  the  cloud  is  carried  into  a  perfectly  dry  atmos- 
phere, such  as  that  existing  in  a  bubble  surrounded  on 
all  sides  by  concentrated  sulphuric  acid,  the  droplets  of 
water  evaporate  and  leave  the  charge  on  a  molecule  of 
air  as  it  was  at  first.  The  20  or  25  per  cent  loss  of  charge 
represents  the  fraction  of  the  droplets  with  their  charges 
which  actually  got  into  contact  with  and  remained  in  the 
liquids  through  which  the  gas  was  being  bubbled. 

In  order  to  find  the  charge  on  each  ion,  Townsend 
took  the  following  five  steps: 

1.  He  assumed  that  in  saturated  water  vapor  each 
ion  condensed  moisture  about  it,  so  that  the  number  of 
ions  was  the  same  as  the  number  of  droplets. 

2.  He  determined  with  the  aid  of  a  quadrant  elec- 
trometer the  total  electrical  charge  per  cubic  centimeter 
carried  by  the  gas. 

3.  He  found  the  total  weight  of  the  cloud  by  passing 
it  through  drying  tubes  and  determining  the  increase  in 
weight  of  these  tubes. 


46  THE  ELECTRON 

4.  He  found  the  average  weight  of  the  water  droplets 
constituting  the  cloud  by  observing  their  rate  of  fall 
under  gravity  and  computing  their  mean  radius  with 
the  aid  of  a  purely  theoretical  law  known  as  Stokes's 
Law. 

5.  He  divided  the  weight  of  the  cloud  by  the  average 
weight  of  the  droplets  of  water  to  obtain  the  number  of 
droplets  which,  if  assumption  i  is  correct,  was  the  number 
of  ions,  and  he  then  divided  the  total  charge  per  cubic 
centimeter  in  the  gas  by  the  number  of  ions  to  find  the 
average  charge  carried  by  each  ion,  that  is.  to  find  e. 

A  brief  description  of  the  way  in  which  these  experi- 
ments were  carried  out  is  contained  in  Appendix  B. 

One  of  the  interesting  side  results  of  this  work  was 
the  observation  that  clouds  from  negative  oxygen  fall 
faster  than  those  from  positive  oxygen,  thus  indicating 
that  the  negative  ions  in  oxygen  act  more  readily  than 
do  the  positive  ions  as  nuclei  for  the  condensation  of 
water  vapor.  This  observation  was  made  at  about  the 
same  time  in  another  way  by  C.  T.  R.  Wilson,1  also  in  the 
Cavendish  Laboratory,  and  it  has  played  a  rather  impor- 
tant role  in  subsequent  work.  Wilson's  discovery  was 
that  when  air  saturated  with  water  vapor  is  ionized  by 
X-rays  from  radioactive  substances  and  then  cooled 
by  a  sudden  expansion,  a  smaller  expansion  is  required 
to  make  a  cloud  form  about  the  negative  than  about  the 
positive  ions.  Thus  when  the  expansion  increased  the 
volume  in  a  ratio  between  1.25  and  1.3,  only  negative 
ions  acted  as  nuclei  for  cloudy  condensation,  while  with 
expansions  greater  than  i .  3  both  negatives  and  positives 
were  brought  down. 

1  Proc.  Camb.  Phil.  Soc.,  IX  (1897),  333. 


EARLY  DETERMINATIONS  OF  e  47 

Townsend  first  obtained  by  the  foregoing  method, 
when  he  worked  with  positive  oxygen, 

e—2  .8Xio~10  electrostatic  units, 
and  when  he  worked  with  negative  oxygen, 

e=T) .  j x io~10  electrostatic  units. 

In  later  experiments1  he  obtained  2.4  and  2.9,  respec- 
tively, in  place  of  the  numbers  given  above,  but  in  view 
of  the  unavoidable  errors,  he  concluded  that  the  two 
charges  might  be  considered  equal  and  approximately 
3Xio~10  electrostatic  units.  Thus  he  arrived  at  about 
the  same  value  for  e  as  that  which  was  then  current  be- 
cause of  the  kinetic  theory  estimates  of  n,  the  number  of 
molecules  in  a  cubic  centimeter  of  a  gas. 

The  weak  points  in  this  first  attempt  at  a  direct 
determination  of  e  consisted  in:  (i)  the  assumption  that 
the  number  of  ions  is  the  same  as  the  number  of  drops; 
(2)  the  assumption  of  Stokes's  Law  of  Fall  which  had 
never  been  tested  experimentally,  and  which  from  a 
theoretical  standpoint  might  be  expected  to  be  in  error 
when  the  droplets  were  small  enough;  (3)  the  assump- 
tion that  the  droplets  were  all  alike  and  fell  at  a  uniform 
rate  wholly  uninfluenced  by  evaporation  or  other  causes 
of  change;  (4)  the  assumption  of  no  convection  currents 
in  the  gas  when  the  rate  of  fall  of  the  cloud  was  being 
measured. 

ii.    SIR  JOSEPH  THOMSON'S  WORK  ON  e 

This  first  attempt  to  measure  e  was  carried  out  in  Pro- 
fessor J.  J.  Thomson's  laboratory.  The  second  attempt 
was  made  by  Professor  Thomson  himself2  by  a  method 

1Proc.  Camb.  Phil.  Soc.,  IX  (1897),  345. 
*  Phil.  Mag.,  XL VI  (1898),  528. 


48  THE  ELECTRON 

which  resembled  Townsend's  very  closely  in  all  its  essen- 
tial particulars.  Indeed,  we  may  set  down  for  Professor 
Thomson's  experiment  precisely  the  same  five  elements 
which  are  set  down  on  p.  45  for  Townsend's.  The  differ- 
ences lay  wholly  in  step  2,  that  is,  in  the  way  in  which 
the  electrical  charge  per  cubic  centimeter  carried  by  the 
gas  was  determined,  and  in  step  3,  that  is,  in  the  way 
in  which  the  total  weight  of  the  cloud  was  obtained. 
Thomson  produced  ions  in  the  space  A  (Fig.  i)  by  an 
X-ray  bulb  which  ran  at  a  constant  rate  and  measured 
first  the  current  which  under  the  influence  of  a  very  weak 
electromotive  force  E  flows  through  A  between  the  sur- 
face of  the  water  and  the  aluminum  plate  which  closes 
the  top  of  the  vessel.  Then  if  n'  is  the  whole  number  of 
ions  of  one  sign  per  cubic  centimeter,  u  the  velocity  of 
the  positive  and  v  that  of  the  negative  ion  under  unit 
electric  force,  i.e.,  if  u  and  v  are  the  mobilities  of  the  posi- 
tive and  negative  ions,  respectively,  then  the  current/ 
per  unit  area  is  evidently  given  by 

I=n'e(u+v)E (4) 

7  and  E  were  easily  measured  in  any  experiment; 
u-\-v  was  already  known  from  Rutherford's  previous 
work,  so  that  n'e,  the  charge  of  one  sign  per  cubic  centi- 
meter of  gas  under  the  ionizing  action  of  a  constant 
source  of  X-rays,  could  be  obtained  at  once  from  (4). 
This  then  simply  replaces  Townsend's  method  of  obtain- 
ing the  charge  per  cubic  centimeter  on  the  gas,  and  in 
principle  the  two  methods  are  quite  the  same,  the  differ- 
ence in  experimental  arrangements  being  due  to  the  fact 
that  Townsend's  ions  are  of  but  one  sign  while  Thom- 
son's are  of  both  signs. 


EARLY  DETERMINATIONS  OF  e  40 

Having  thus  obtained  n'e  of  equation  (4),  Thomson 
had  only  to  find  nr  and  then  solve  for  e.  To  obtain  n' 
he  proceeded  exactly  as  Townsend  nad  done  in  letting 
the  ions  condense  droplets  of  water  about  them  and 
weighing  the  cloud  thus  formed.  But  in  order  to  form 
the  cloud,  Thomson  utilized  C.  T.  R.  Wilson's  discovery 


FIG.  i 

just  touched  upon  above,  that  a  sudden  expansion  and 
consequent  cooling  of  the  air  in  A  (Fig.  i)  would  cause 
the  ions  in  A  to  act  as  nuclei  for  the  formation  of  water 
droplets.  To  produce  this  expansion  the  piston  P  is 
suddenly  pulled  down  so  as  to  increase  the  volume  of  the 
space  above  it.  A  cloud  is  thus  formed  about  the  ions 
in  A.  Instead  of  measuring  the  weight  of  this  cloud 
directly,  as  Townsend  had  done,  Thomson  computed  it 
by  a  theoretical  consideration  of  the  amount  of  cooling 


50  THE  ELECTRON 

produced  by  the  expansion  and  the  known  difference 
between  the  densities  of  saturated  water  vapor  at  the 
temperature  of  the  room  and  the  temperature  resulting 
from  the  expansion.  This  method  of  obtaining  the 
weight  of  the  cloud  was  less  direct  and  less  reliable  than 
that  used  by  Townsend,  but  it  was  the  only  one  avail- 
able with  Thomson's  method  of  obtaining  an  ionized  gas 
and  of  measuring  the  charge  per  cubic  centimeter  on  that 
gas.  The  average  size  of  the  droplets  was  obtained  pre- 
cisely as  in  Townsend's  work  by  applying  Stokes's  Law 
to  the  observed  rate  of  fall  of  the  top  of  the  cloud  in 
chamber  A. 

The  careful  consideration  of  Thomson's  experiment 
shows  that  it  contains  all  the  theoretical  uncertainties 
involved  in  Townsend's  work,  while  it  adds  considerably 
to  the  experimental  uncertainties.  The  most  serious  of 
the  theoretical  uncertainties  arise  from  (i)  the  assump- 
tion of  Stokes's  Law,  and  (2)  the  assumption  that  the 
number  of  ions  is  equal  to  the  number  of  droplets.  Both 
observers  sought  for  some  experimental  justification  for 
the  second  and  most  serious  of  these  assumptions,  but 
subsequent  work  by  H.  A.  Wilson,  by  Quincke,  and 
by  myself  has  shown  that  clouds  formed  by  C.  T.  R. 
Wilson's  method  consist  in  general  of  droplets  some  of 
which  may  carry  one,  some  two,  some  ten,  or  almost  any 
number  of  unit  charges,  and  I  have  never  been  able, 
despite  quite  careful  experimenting,  to  obtain  conditions 
in  which  it  was  even  approximately  true  that  each 
droplet  carried  but  a  single  unit  charge.  Quincke  has 
recently  published  results  from  which  he  arrives  at  the 
same  conclusion,1 

1  Verh.  der  deutsch.  phys.  Ges.,  XVI  (1914),  422. 


EARLY  DETERMINATIONS  OF  e  51 

Again,  when  we  compare  the  experimental  uncer- 
tainties in  Townsend's  and  Thomson's  work,  it  is  at  once 
obvious  that  the  assumption  that  the  clouds  are  not 
evaporating  while  the  rate  of  fall  is  being  determined  is 
even  more  serious  in  Thomson's  experiment  than  in 
Townsend's,  for  the  reason  that  in  the  former  case  the 
clouds  are  formed  by  a  sudden  expansion  and  a  conse- 
quent fall  in  temperature,  and  it  is  certain  that  during 
the  process  of  the  return  of  the  temperature  to  initial 
conditions  the  droplets  must  be  evaporating.  Further- 
more, this  sudden  expansion  makes  the  likelihood  of  the 
existence  of  convection  currents,  which  would  falsify 
the  computations  of  the  radius  of  the  drop  from  the  ob- 
served rate  of  fall,  more  serious  in  Thomson's  work  than 
in  Townsend's.  The  results  which  Thomson  attained 
in  different  experiments  gave  values  ranging  from 
5.5Xio~10  to  8.4Xio~10.  He  published  as  his  final 
value  6 .  5X  io~10.  In  1903,  however,1  he  published  some 
new  work  on  e  in  which  he  had  repeated  the  determina- 
tion, using  the  radiation  from  radium  in  place  of  that 
from  X-rays  as  his  ionizing  agent  and  obtained  the  result 
e  —  3.4Xio~10.  He  explained  the  difference  by  the 
assumption  that  in  his  preceding  work  the  more  active 
negative  ions  had  monopolized  the  aqueous  vapor  avail- 
able and  that  the  positive  ions  had  not  been  brought 
down  with  the  cloud  as  he  had  before  assumed  was.  the 
case.  He  now  used  more  sudden  expansions  than  he 
had  used  before,  and  concluded  that  the  assumption 
made  in  the  earlier  experiments  tnat  the  number  of  ions 
was  equal  to  the  number  of  particles,  although  shown  to 
be  incorrect  for  the  former  case,  was  correct  for  these 

1  Phil.  Mag.,  V  (1903;  6th  series),  354. 


52  .      THE  ELECTRON 

second  experiments.  As  a  matter  of  fact,  if  he  had 
obtained  only  half  the  ions  in  the  first  experiments  and 
all  of  them  in  the  second,  his  second  result  should  have 
come  out  approximately  one-half  as  great  as  the  first, 
which  it  actually  did.  Although  Thomson's  experiment 
was  an  interesting  and  important  modification  of  Town- 
send  's,  it  can  scarcely  be  said  to  have  added  greatly 
to  the  accuracy  of  our  knowledge  of  e. 

The  next  step  in  advance  in  the  attempt  at  the  deter- 
mination of  e  was  made  in  1903  by  H.  A.  Wilson,1  also 
in  the  Cavendish  Laboratory. 

III.      H.  A.   WILSON'S  METHOD 

Wilson's  modification  of  Thomson's  work  consisted  in 
placing  inside  the  chamber  A  two  horizontal  brass  plates 
3^  cm.  in  diameter  and  from  4  to  10  mm.  apart  and  con- 
necting to  these  plates  the  terminals  of  a  2,000- volt 
battery.  He  then  formed  a  negative  cloud  by  a  sudden 
expansion  of  amount  between  1.25  and  1.3,  and 
observed  first  the  rate  of  fall  of  the  top  surface  of  this 
cloud  between  the  plates  when  no  electrical  field  was 
on;  then  he  repeated  the  expansion  and  observed  the 
rate  of  fall  of  the  cloud  when  the  electrical  field  as  well 
as  gravity  was  driving  the  droplets  downward.  If  mg 
represents  the  force  of  gravity  acting  on  the  droplets  in 
the  top  surface  of  the  cloud  and  mg+Fe  the  force  of 
gravity  plus  the  electrical  force  arising  from  the  action 
of  the  field  F  on  the  charge  e,  and  if  vt  is  the  velocity 
of  fall  under  the  action  of  gravity  alone,  and  v9  the 
velocity  when  both  gravity  and  the  electrical  field  are 
acting,  then,  if  the  ratio  between  the  force  acting  and 

lOp.  dl.,  p.  47Q. 


EARLY  DETERMINATIONS  OF  e  53 

the  velocity  produced  is  the  same  when  the  particle  is 
charged  as  when  it  is  uncharged,  we  have 


l 
mg+Fe 


Combining  this  with  the  Stokes's  Law  equation  which 
runs 


9    -n 

in  which  a  is  the  radius,  a  the  density,  t>x  the  velocity  of 
the  drop  under  gravity  #,.  and  77  is  the  viscosity  of  the  air, 
and  then  eliminating  m  by  means  of 

m  =  frra3o-  ......  ,.....:  ........  (7) 

Wilson  obtained  after  substituting  for  17  and  <j  the  appro- 
priate values  (not  accurately  known,  it  is  true,  for 
saturated  air  at  the  temperature  existing  immediately 
after  the  expansion), 


(8) 


Wilson's  method  constitutes  a  real  advance  in  that  it 
eliminates  the  necessity  of  making  the  very  awkward 
assumption  that  the  number  of  droplets  is  equal  to  the 
number  of  negative  ions,  for  since  he  observes  only  the 
rate  of  fall  of  the  top  of  the  cloud,  and  since  the  more 
heavily  charged  droplets  will  be  driven  down  more 
rapidly  by  the  field  than  the  less  heavily  charged  ones, 
his  actual  measurements  would  always  be  made  upon 
the  least  heavily  charged  droplets.  All  of  the  other  dif- 
ficulties and  assumptions  contained  in  either  Town- 
send's  or  Thomson's  experiments  inhere  also  in  Wilson's, 
and  in  addition  one  fresh  and  rather  serious  assumption 


54  THE  ELECTRON 

is  introduced,  namely,  that  the  clouds  formed  in  succes- 
sive expansions  are  identical  as  to  size  of  droplets.  For 
we  wrote  down  the  first  equation  of  Wilson's  method  as 
though  the  vt  and  v2  were  measurements  made  upon 
the  same  droplet,  when  as  a  matter  of  fact  the  measure- 
ments are  actually  made  on  wholly  different  droplets. 
I  have  myself  found  the  duplication  of  cloud  conditions 
in  successive  expansions  a  very  uncertain  matter. 
Furthermore,  Wilson's  method  assumes  uniformity  in  the 
field  between  the  plates,  an  assumption  which  might  be 
quite  wide  of  the  truth. 

Although  the  elimination  of  the  assumption  of 
equality  of  the  number  of  droplets  and  the  number  of 
ions  makes  Wilson's  determination  of  e  more  reliable  as 
to  method  than  its  predecessors,  the  accuracy  actually 
attained  was  not  great,  as  can  best  be  seen  from  his  own 
final  summary  of  results.  He  made  eleven  different 
determinations  which  varied  from  £=2Xio~10  to 
e=4.4Xio~10.  His  eleven  results  are: 

TABLE  I 

e  •  e 

2.3Xio~10  3.8X10-'° 

2.6  «  3.0        " 

4-4        "  3-5        " 

2.7  "  2.0        " 

3-4        "  2.3        " 

3-8        "  

Mean       3.iXio~10 

In  1906,  being  dissatisfied  with  the  variability  of  these 
results,  the  author  repeated  Wilson's  experiment  without 
obtaining  any  greater  consistency  than  that  which  the 
latter  had  found.  Indeed,  the  instability,  distortion,  and 
indefiniteness  of  the  top  surface  of  the  cloud  were  some- 


EARLY  DETERMINATIONS  OF  e  55 

what  disappointing,  and  the  results  were  not  considered 
worth  publishing.  Nevertheless,  it  was  concluded  from 
these  observations  that  the  accuracy  might  be  improved 
by  using  radium  instead  of  X-rays  for  the  ionizing  agent, 
by  employing  stronger  electrical  fields,  and  thus  increas- 
ing the  difference  between  Vj.  and  v2,  which  in  Wilson's 
experiment  had  been  quite  small,  and  by  observing  the 
fall  of  the  cloud  through  smaller  distances  and  shorter 
times  in  order  to  reduce  the  error  due  to  the  evapora- 
tion of  the  cloud  during  the  time  of  observation. 
Accordingly,  a  4,ooo-volt  storage  battery  was  built  and 
in  the  summer  of  1908  Mr.  Begeman  and  the  author, 
using  radium  as  the  ionizing  agent,  again  repeated  the 
experiment  and  published  some  results  which  were  some- 
what more  consistent  than  those  reported  by  Wilson.1 
We  gave  as  the  mean  of  ten  observations  which  varied 
from 3. 66  to  4.37  the  value  e=4.o6Xio~10.  We  stated 
at  the  time  that  although  we  had  not  eliminated  alto- 
gether the  error  due  to  evaporation,  we  thought  that  we 
had  rendered  it  relatively  harmless,  and  that  our  final 
result,  although  considerably  larger  than  either  Wilson's 
or  Thomson's  (3.1  and  3.4,  respectively),  must  be  con- 
sidered an  approach  at  least  toward  the  correct  value. 

IV.      THE  BALANCED-DROP  METHOD 

Feeling,  however,  that  the  amount  of  evaporation  of 
the  cloud  was  still  a  quite  unknown  quantity,  I  next 
endeavored  to  devise  a  way  of  eliminating  it  entirely. 
The  plan  now  was  to  use  an  electrical  field  which  was 
strong  enough,  not  merely  to  increase  or  decrease  slightly 
the  speed  of  fall  under  gravity  of  the  top  surface  of  the 

'  Phys.  Rev.,  XXVI  (1908),  198. 


56  THE  ELECTRON 

cloud,  as  had  been  done  in  all  the  preceding  experiments, 
but  also  sufficiently  strong  to  hold  the  top  surface  of  the 
cloud  stationary,  so  that  the  rate  of  its  evaporation  could 
be  accurately  observed  and  allowed  for  in  the  computa- 
tions. 

This  attempt,  while  not  successful  in  the  form  in 
which  it  had  been  planned,  led  to  a  modification  of  the 
cloud  method  which  seemed  at  the  time,  and  which  has 
actually  proved  since,  to  be  of  far-reaching  importance. 
//  made  it  for  the  first  time  possible  to  make  all  the  measure- 
ments on  individual  droplets,  and  thus  not  merely  to 
eliminate  ultimately  all  of  the  questionable  assumptions 
and  experimental  uncertainties  involved  in  the  cloud 
method  of  determining  e,  but,  more  important  still,  it 
made  it  possible  to  examine  the  properties  of  individual 
isolated  electrons  and  to  determine  whether  different 
ions  actually  carry  one  and  the  same  charge.  That  is 
to  say,  it  now  became  possible  to  determine  whether 
electricity  in  gases  and  solutions  is  actually  built  up  out 
of  electrical  atoms,  each  of  which  has  exactly  the  same 
value,  or  whether  the  electron  which  had  first  made  its 
appearance  in  Faraday's  experiments  on  solutions  and 
then  in  Townsend's  and  Thomson's  experiments  on  gases 
is  after  all  only  a  statistical  mean  of  charges  which  are 
themselves  greatly  divergent.  This  latter  view  had  been 
strongly  urged  up  to  and  even  after  the  appearance  of 
the  work  which  is  now.  under  consideration.  It  will  be 
given  further  discussion  presently. 

The  first  determination  which  was  made  upon  the 
charges  carried  by  individual  droplets  was  carried  out 
in  the  spring  of  1909.  A  report  of  it  was  placed  upon 
the  program  of  the  British  Association  meeting  at  Winni- 


EARLY  DETERMINATIONS  OF  e  57 

peg  in  August,  1909,  as  an  additional  paper,  was  printed 
in  abstract  in  the  Physical  Review  for  December,  1909, 
and  in  full  in  the  Philosophical  Magazine  for  February, 
1910,  under  the  title  "A  New  Modification  of  the  Cloud 
Method  of  Determining  the  Elementary  Electrical 
Charge  and  the  Most  Probable  Value  of  That  Charge.7'1 
The  following  extracts  from  that  paper  show  clearly  what 
was  accomplished  in  this  first  determination  of  the 
charges  carried  by  individual  droplets. 

THE  BALANCING  OF  INDIVIDUAL  CHARGED  DROPS  BY  AN 
ELECTROSTATIC   FIELD 

My  original  plan  for  eliminating  the  evaporation  error  was  to 
obtain,  if  possible,  an  electric  field  strong  enough  exactly  to  balance 
the  force  of  gravity  upon  the  cloud  and  then  by  means  of  a  sliding 
contact  to  vary  the  strength  of  this  field  so  as  to  hold  the  cloud 
balanced  throughout  its  entire  life.  In  this  way  it  was  thought 
that  the  whole  evaporation-history  of  the  cloud  might  be  recorded, 
and  that  suitable  allowances  might  then  be  made  in  the  observa- 
tions on  the  rate  of  fall  to  eliminate  entirely  the  error  due  to 
evaporation.  It  was  not  found  possible  to  balance  the  cloud,  as 
had  been  originally  planned,  but  it  was  found  possible  to  do  some- 
thing much  better:  namely,  to  hold  individual  charged  drops  sus- 
pended by  the  field  for  periods  varying  from  30  to  60  seconds. 
I  have  never  actually  timed  drops  which  lasted  more  than  45 
seconds,  although  I  have  several  times  observed  drops  which  in 
my  judgment  lasted  considerably  longer  than  this:  The  drops 
which  it  was  found  possible  to  balance  by  an  electrical  field  always 
carried  multiple  charges,  and  the  difficulty  experienced  in  balan- 
cing such  drops  was  less  than  had  been  anticipated. 

The  procedure  is  simply  to  form  a  cloud  and  throw  on  the 
field  immediately  thereafter.  The  drops  which  have  charges  of 
the  same  sign  as  that  of  the  upper  plate  or  too  weak  charges  of  the 
opposite  sign  rapidly  fall,  while  those  which  are  charged  with  too 
many  multiples  of  the  sign  opposite  to  that  of  the  upper  plate  are 

1  Phil.  Mag.,  XIX  (1910),  209. 


58  THE  ELECTRON 

jerked  up  against  gravity  to  this  plate.  The  result  is  that  after 
a  lapse  of  7  or  8  seconds  the  field  of  view  has  become  quite  clear 
save  for  a  relatively  small  number  pf  drops  which  have  just  the 
right  ratio  of  charge  to  mass  to  be  held  suspended  by  the  electric 
field.  These  appear  as  perfectly  distinct  bright  points.  I  have 
on  several  occasions  obtained  but  one  single  such  "star"  in  the 
whole  field  and  held  it  there  for  nearly  a  minute.  For  the  most 
part,  however,  the  observations  recorded  below  were  made  with 
a  considerable  number  of  such  points  in  view.  Thin,  flocculent 
clouds,  the  production  of  which  seemed  to  be  facilitated  by  keep- 
ing the  water-jackets  /i  and  72  (Fig.  2)  a  degree  or  two  above  the 
temperature  of  the  room,  were  found  to  be  particularly  favorable 
to  observations  of  this  kind. 

Furthermore,  it  was  found  possible  so  to  vary  the  mass  of  a 
drop  by  varying  the  ionization,  that  drops  carrying  in  some  cases 
two,  in  some  three,  in  some  four,  in  some  five,  and  in  some  six, 
multiples  could  be  held  suspended  by  nearly  the  same  field.  The 
means  of  gradually  varying  the  field  which  had  been  planned  were 
therefore  found  to  be  unnecessary.  If  a  given  field  would  not 
hold  any  drops  suspended  it  was  varied  by  steps  of  100  or  200 
volts  until  drops  were  held  stationary,  or  nearly  stationary.  When 
the  P.D.  was  thrown  off  it  was  often  possible  to  see  different  drops 
move  down  under  gravity  with  greatly  different  speeds,  thus  show- 
ing that  these  drops  had  different  masses  and  correspondingly 
different  charges. 

The  life-history  of  these  drops  is  as  follows:  If  they  are  a 
little  too  heavy  to  be  held  quite  stationary  by  the  field  they  begin 
to  move  slowly  down  under  gravity.  Since,  however,  they  slowly 
evaporate,  their  downward  motion  presently  ceases,  and  they 
become  stationary  for  a  considerable  period  of  time.  Then  the 
field  gets  the  better  of  gravity  and  they  move  slowly  upward. 
Toward  the  end  of  their  life  in  the  space  between  the  plates,  this 
upward  motion  becomes  quite  rapidly  accelerated  and  they  are 
drawn  with  considerable  speed  to  the  upper  plate.  This,  taken 
in  connection  with  the  fact  that  their  whole  life  between  plates 
only  4  or  5  mm.  apart  is  from  35  to  60  seconds,  will  make  it  obvious 
that  during  a  very  considerable  fraction  of  this  time  their  motion 
must  be  exceedingly  slow.  I  have  often  held  drops  through  a 


EARLY  DETERMINATIONS  OF  e  59 

period  of  from  10  to  15  seconds,  during  which  it  was  impossible  to 
see  that  they  were  moving  at  all.  Shortly  after  an  expansion  I 
have  seen  drops  which  at  first  seemed  stationary,  but  which  then 
began  to  moveslowly  down  in  the  direction  of  gravity,  then  become 
stationary  again,  then  finally  began  to  move  slowly  up.  This  is 
probably  due  to  the  fact  that  large  multiply  charged  drops  are  not 
in  equilibrium  with  smaller  singly  charged  drops  near  them,  and 
hence,  instead  of  evaporating,  actually  grow  for  a  time  at  the 
expense  of  their  small  neighbors.  Be  this  as  it  may,  however,  it 
is  by  utilizing  the  experimental  fact  that  there  is  a  considerable 
period  during  which  the  drops  are  essentially  stationary  that  it 
becomes  possible  to  make  measurements  upon  the  rate  of  fall  in 
which  the  error  due  to  evaporation  is  wholly  negligible  hi  compari- 
son with  the  other  errors  of  the  experiment.  Furthermore,  in 
making  measurements  of  this  kind  the  observer  is  just  as  likely 
to  time  a  drop  which  has  not  quite  reached  its  stationary  point  as 
one  which  has  just  passed  through  that  point,  so  that  the  mean  of 
a  considerable  number  of  observations  would,  even  from  a  theo- 
retical standpoint,  be  quite  free  from  an  error  due  to  evaporation. 

THE   METHOD    OF   OBSERVATION 

The  observations  on  the  rate  of  fall  were  made  with  a  short- 
focus  telescope  T  (see  Fig.  2)  placed  about  2  feet  away  from  the 
plates.  In  the  eyepiece  of  this  telescope  were  placed  three  equally 
spaced  cross-hairs,  the  distance  between  those  at  the  extremes  cor- 
responding to  about  one-third  of  the  distance  between  the  plates. 
A  small  section  of  the  space  between  the  plates  was  illuminated  by 
a  narrow  beam  from  an  arc  light,  the  heat  of  the  arc  being  absorbed 
by  three  water  cells  in  series.  The  air  between  the  plates  was 
ionized  by  200  mg.  of  radium,  of  activity  20,000,  placed  from 
3  to  10  cm.  away  from  the  plates.  A  second  or  so  after  expansion 
the  radium  was  removed,  or  screened  off  with  a  lead  screen,  and  the 
field  thrown  on  by  hand  by  means  of  a  double-throw  switch.  If 
drops  were  not  found  to  be  held  suspended  by  the  field,  the  P.D. 
was  changed  or  the  expansion  varied  until  they  were  so  held.  The 
cross-hairs  were  set  near  the  lower  plate,  and  as  soon  as  a  stationary 
drop  was  found  somewhere  above  the  upper  cross-hair,  it  was 
watched  for  a  few  seconds  to  make  sure  that  it  was  not  moving, 


6o 


THE  ELECTRON 


and  then  the  field  was  thrown  off  and  the  plates  short-circuited 
by  means  of  the  double-throw  switch,  so  as  to  make  sure  that  they 
retained  no  charge.  The  drop  was  then  timed  by  means  of  an 
accurate  stop  watch  as  it  passed  across  the  three  ^ross-hairs,  one 
of  the  two  hands  of  the  watch  being  stopped  at  the  instant  of 


FIG. 


passage  across  the  middle  cross-hair,  the  other  at  the  instant  of 
passage  across  the  lower  one.  It  will  be  seen  that  this  method 
of  observation  furnishes  a  double  check  upon  evaporation;  for  if 
the  drop  is  stationary  at  first,  it  is  not  evaporating  sufficiently  to 
influence  the  reading  of  the  rate  of  fall,  and  if  it  begins  to  evaporate 
appreciably  before  the  reading  is  completed,  the  time  required  to 
pass  through  the  second  space  should  be  greater  than  that  required 


EARLY  DETERMINATIONS  OF  e  61 

to  pass  through  the  first  space.  It  will  be  seen  from  the  observa- 
tions which  follow  that  this  was  not,  in  general,  the  case. 

It  is  an  exceedingly  interesting  and  instructive  experiment  to 
watch  one  of  these  drops  start  and  stop,  or  even  reverse  its  direc- 
tion of  motion,  as  the  field  is  thrown  off  and  on.  I  have  often 
caught  a  drop  which  was  just  too  light  to  remain  stationary  and 
moved  it  back  and  forth  in  this  way  four  or  five  times  between  the 
same  two  cross-hairs,  watching  it  first  fall  under  gravity  when  the 
field  was  thrown  off  and  then  rise  against  gravity  when  the  field 
was  thrown  on.  The  accuracy  and  certainty  with  which  the 
instants  of  passage  of  the  drops  across  the  cross-hairs  can  be  deter- 
mined are  precisely  the  same  as  that  obtainable  in  timing  the 
passage  of  a  star  across  the  cross-hairs  of  a  transit  instrument. 

Furthermore,  since  the  observations  upon  the  quantities 
occurring  in  equation  (4)  [see  (8)  p.  53  of  this  volume]  are  all 
made  upon  the  same  drop,  all  uncertainties  as  to  whether  condi- 
tions can  be  exactly  duplicated  in  the  formation  of  successive 
clouds  obviously  disappear.  There  is  no  theoretical  uncertainty 
whatever  left  in  the  method  unless  it  be  an  uncertainty  as  to 
whether  or  not  Stokes's  Law  applies  to  the  rate  of  fall  of  these 
drops  under  gravity.  The  experimental  uncertainties  are  reduced 
to  the  uncertainty  in  a  time  determination  of  from  3  to  5  seconds, 
when  the  object  being  timed  is  a  single  moving  bright  point.  This 
means  that  when  the  time  interval  is  say  5  seconds,  as  it  is  in  some 
of  the  observations  given  below,  the  error  which  a  practiced 
observer  will  make  with  an  accurate  stop  watch  in  any  particular 
observation  will  never  exceed  2  parts  in  50.  The  error  in  the  mean 
of  a  considerable  number  of  concordant  observations  will  obviously 
be  very  much  less  than  this. 

Since  in  this  form  of  observation  the  v3  of  equation  (5)  [(8)  of 
this  volume]  is  zero,  and  since  F  is  negative  in  sign,  equation  (5) 
reduces  to  the  simple  form: 

y 

X-(*>i)*  .................   (6)' 


XI  had  changed  the  constant  in  Wilson's  equation  from  3.1  to 
3.422  because  of  careful  measurements  on  the  temperature  existing  in 
the  cloud  chamber  about  10  seconds  after  expansion  and  because  of  new 
measurements  on  the  viscosity  of  the  saturated  air. 


62 


THE  ELECTRON 


It  will  perhaps  be  of  some  interest  to  introduce  two 
tables  from  this  paper  to  show  the  exact  nature  of  these 


SERIES    i    (BALANCED    POSITIVE 
WATER  DROPS) 

Distance  between  plates  .  545  cm. 
Measured  distance  of  fall  .155  cm. 


TABLE  II 

SERIES 


2    (BALANCED    POSITIVE 
WATER  DROPS) 

Distance  between  plates  .  545  cm. 
Measured  distance  of  fall  .155  cm. 


Volts 

Time 
i  Space 

Time 
2  Spaces 

2,  28^.  . 

2  .  4  sec. 

4  8  sec. 

2,281?.  . 

2.4 

4  8 

2,27<\  .  . 

2.4 

4.8 

2  32S 

2   4, 

4.   8 

2  32"? 

2    6 

4  8 

2,32^ 

2    2 

4  8 

2,36^  .  . 

2    4 

4  8 

2  312 

2    4 

4  8 

Mean  time  for  .155  cm.  =  4. 


14.14 
=  13.77x10-10 

Therefore  6=13. 85X10-1' 
=4.59X10-10. 


sec. 
I 


Volts 

Time 
i  Space 

Time 
2  Spaces 

2,36^     . 

i  8  sec. 

4  O  sec. 

2,365  

2,365  

1.8 
2  .  2 

4.0 
3.8 

2,^6< 

i  8 

4O 

2,3Q<     . 

2    O 

4-  O 

2,^qr 

2    O 

4  ° 

2,395  .  . 

2  .O 

3  8 

2  ?6<C 

I    8 

4O 

2  36^ 

I    8 

4O 

2,365;     . 

i  8 

4  O 

2,374  

1  .90 

^.06 

Mean  time  for  .155  cm.  =  3. 91  sec. 


=  18.25X10-10 
Therefore  6  =  18.25-7-4 

=  4.56X1010. 

TABLE  III 


Series 

Charge 

Value  of  e 

Weight 
Assigned 

I  

~\e 

4  59 

7 

2  

40 

4-  56 

7 

ie 

4  64 

6 

4" 

Cg 

4  83 

4 

f  .  . 

2g 

4.87 

i 

6 

6e 

4   60 

•j 

Simple  mean  6  =  4.70X10— I0 
Weighted  mean  6=4.65X10-10 


EARLY  DETERMINATIONS  OF  e  63 

earliest  measurements  on  the  charges  carried  by  indi- 
vidual particles. 

In  connection  with  these  experiments  I  chanced  to 
observe  a  phenomenon  which  interested  me  very  much 
at  the  time  and  suggested  quite  new  possibilities.  While 
working  with  these  "  balanced  drops "  I  noticed  on  sev- 
eral occasions  on  which  I  had  failed  to  screen  off  the  rays 
from  the  radium  that  now  and  then  one  of  them  would 
suddenly  change  its  charge  and  begin  to  move  up  or 
down  in  the  field,  evidently  because  it  had  captured  in 
the  one  case  a  positive,  in  the  other  a  negative,  ion.  This 
opened  up  the  possibility  of  measuring  with  certainty., 
not  merely  the  charges  on  individual  droplets  as  I  had 
been  doing,  but  the  charge  carried  by  a  single  atmos- 
pheric ion.  For  by  taking  two  speed  measurements  on  the 
same  drop,  one  before  and  one  after  it  had  caught  an  ion,  I 
could  obviously  eliminate  entirely  the  properties  of  the  drop 
and  of  the  medium  and  deal  with  a  quantity  which  was  pro- 
portional merely  to  the  charge  on  the  captured  ion  itself. 

Accordingly,  in  the  fall  of  1909  there  was  started  the 
series  of  experiments  described  in  the  succeeding  chapter. 

The  problem  had  already  been  so  nearly  solved  by 
the  work  with  the  water  droplets  that  there  seemed  no 
possibility  of  failure.  It  was  only  necessary  to  get  a 
charged  droplet  entirely  free  from  evaporation  into  the 
space  between  the  plates  of  a  horizontal  air  condenser 
and  then,  by  alternately  throwing  on  and  off  an  electrical 
field,  to  keep  this  droplet  pacing  its  beat  up  and  down 
between  the  plates  until  it  could  catch  an  atmospheric 
ion  in  just  the  way  I  had  already  seen  the  water  droplets 
do.  The  change  in  the  speed  in  the  field  would  then  be 
exactly  proportional  to  the  charge  on  the  ion  captured. 


CHAPTER  IV 

GENERAL  PROOF  OF  THE  ATOMIC  NATURE  OF 
ELECTRICITY 

Although  the  " balanced-droplet  method''  just  de- 
scribed had  eliminated  the  chief  sources  of  uncertainty 
which  inhered  in  preceding  work  on  e  and  had  made  it 
possible  to  assert  with  much  confidence  that  the  unit 
charge  was'  a  real  physical  entity  and  not  merely  a 
"  statistical  mean,"  it  was  yet  very  far  from  an  exact 
method  of  studying  the  properties  of  gaseous  ions.  The 
sources  of  error  or  uncertainty  which  still  inhered  in  it 
arose  from  (i)  the  lack  of  stagnancy  in  the  air  through 
which  the  drop  moved ;  (2)  the  lack  of  perfect  uniformity 
of  the  electrical  field  used;  (3)  the  gradual  evaporation 
of  the  drops,  rendering  it  impossible  to  hold  a  given  drop 
under  observation  for  more  than  a  minute  or  to  time  a 
drop  as  it  fell  under  gravity  alone  through  a  period  of 
more  than  five  or  six  seconds;  and  (4)  the  assumption 
of  the  validity  of  Stokes's  Law. 

The  method  which  was  devised  to  replace  it  was  not 
only  entirely  free  from  all  of  these  limitations,  but  it 
constituted  an  entirely  new  way  of  studying  ionization 
and  one  which  at  once  yielded  important  results  in  a 
considerable  number  of  directions.  This  chapter  deals 
with  some  of  these  by-products  of  the  determination  of 
e  which  are  of  even  more  fundamental  interest  and 
importance  than  the  mere  discovery  of  the  exact  size  of 
the  electron. 

64 


ATOMIC  NATURE  OF  ELECTRICITY  65 

I.      ISOLATION    OF    INDIVIDUAL    IONS   AND   MEASUREMENT 
OF   THEIR  RELATIVE   CHARGES 

In  order  to  compare  the  charges  on  different  ions,  the 
procedure  adopted  was  to  blow  with  an  ordinary  com- 
mercial atomizer  an  oil  spray  into  the  chamber  C  (Fig.  3). 


FIG.  3 

The  air  with  which  this  spray  was  blown  was  first  ren- 
dered dust-free  by  passage  through  a  tube  containing 
glass  wool.  The  minute  droplets  of  oil  constituting  the 
spray,  most  of  them  having  a  radius  of  the  order  of  a 
one- thousandth  of  a  millimeter,  slowly  fell  in  the  cham- 
ber C,  and  occasionally  one  of  them  would  find  its  way 


66  THE  ELECTRON 

through  the  minute  pinhole  p  in  the  middle  of  the  circular 
brass  plate  M,  22  cm.  in  diameter,  which  formed  one  of 
the  plates  of  the  air  condenser.  The  other  plate,  N,  was 
held  16  mm.  beneath  it  by  three  ebonite  posts  a.  By 
means  of  the  switch  5*  these  plates  could  be  charged,  the 
one  positively  and  the  other  negatively,  by  making  them 
the  terminals  of  a  10,000- volt  storage  battery  B,  while 
throwing  the  switch  the  other  way  (to  the  left)  short- 
circuited  them  and  reduced  the  field  between  them  to  zero. 
The  oil  droplets  which  entered  at  p  were  illuminated  by  a 
powerful  beam  of  light  which  passed  through  diametri- 
cally opposite  windows  in  the  encircling  ebonite  strip  c. 
As  viewed  through  a  third  window  in  c  on  the  side  toward 
the  reader,  it  appeared  as  a  bright  star  on  a  black  back- 
ground. These  droplets  which  entered  p  were  found  in 
general  to  have  been  strongly  charged  by  the  frictional 
process  involved  in  blowing  the  spray,  so  that  when  the 
field  was  thrown  on  in  the  proper  direction  they  would 
be  pulled  up  toward  M .  Just  before  the  drop  under 
observation  could  strike  M  the  plates  would  be  short- 
circuited  and  the  drop  allowed  to  fall  under  gravity  until 
it  was  close  to  N,  when  the  direction  of  motion  would 
be  again  reversed  by  throwing  on  the  field.  In  this  way 
the  drop  would  be  kept  traveling  back  and  forth  between 
the  plates.  The  first  time  the  experiment  was  tried  an 
ion  was  caught  within  a  few  minutes,  and  the  fact  of  its 
capture  was  signaled  to  the  observer  by  the  change 
in  the  speed  with  which  it  moved  up  when  the  field  was 
on.  The  significance  of  the  experiment  can  best  be 
appreciated  by  examination  of  the  complete  record  of 
one  of  the  early  experiments  when  the  timing  was  done 
merely  with  a  stop  watch. 


ATOMIC  NATURE  OF  ELECTRICITY  67 

The  column  headed  tg  gives  the  successive  times  which 
the  droplet  required  to  fall  between  two  fixed  cross-hairs 
in  the  observing  telescope  whose  distance  apart  corre- 
sponded in  this  case  to  an  actual  distance  of  fall  of 
.5222  cm.  It  will  be  seen  that  these  numbers  are  all  the 
same  within  the  limits  of  error  of  a  stop-watch  measure- 
ment. The  column  marked  tF  gives  the  successive  times 

TABLE  IV 

tg  tv 

13-6  12.5 

13.8  12.4 

13.4  21.8 
13-4  34-8 
13.6  84.5 
13-6  85.5 
13-7  34-6 
13-5  34-8 

13.5  16.0 
13-8  34-8 
13-7  34-6 
13.8  21.9 
13-6 

13-5 
13-4 
13-8 
13-4 

Mean  13.595 

which  the  droplet  required  to  rise  under  the  influence  of 
the  electrical  field  produced  by  applying  in  this  case 
5,051  volts  of  potential  difference  to  the  plates  M  and  N. 
It  will  be  seen  that  after  the  second  trip  up,  the  time 
changed  from  12.4  to  21.8,  indicating,  since  in  this  case 
the  drop  was  positive,  that  a  negative  ion  had  been 
caught  from  the  air.  The  next  time  recorded  under  //?, 
namely,  34.8,  indicates  that  another  negative  ion  had 
been  caught.  The  next  time,  84 . 5,  indicates  the  capture 


68  THE  ELECTRON 

of  still  another  negative  ion.  This  charge  was  held 
for  two  trips,  when  the  speed  changed  back  again  to 
34.6,  showing  that  a  positive  ion  had  now  been  caught 
which  carried  precisely  the  same  charge  as  the  negative 
ion  which  before  caused  the  inverse  change  in  time,  i.e., 
that  from  34.8  to  84.5. 

In  order  to  obtain  some  of  the  most  important  con- 
sequences of  this  and  other  similar  experiments  we 
need  make  no  assumption  further  than  this,  that  the 
velocity  with  which  the  drop  moves  is  proportional  to 
the  force  acting  upon  it  and  is  independent  of  the  elec- 
trical charge  which  it  carries.  Fortunately  this  assump- 
tion can  be  put  to  very  delicate  experimental  test,  as  will 
presently  be  shown,  but  introducing  it  for  the  time  being 
as  a  mere  assumption,  as  Townsend,  Thomson,  and 
Wilson  had  done  before,  we  get 

^1         nig  mg(  ,  ^ 

=  -=^(i>x+%)  .........   (9) 


V2    Fen—mg  Fvj 

The  negative  sign  is  used  in  the  denominator  because  v2 
will  for  convenience  be  taken  as  positive  when  the  drop 
is  going  up  in  the  direction  of  Ft  while  z>x  will  be  taken 
as  positive  when  it  is  going  down  in  the  direction  of  g. 
en  denotes  the  charge  on  the  drop,  and  must  not  be  con- 
fused with  the  charge  on  an  ion.  If  now  by  the  capture 
of  an  ion  the  drop  changes  its  charge  from  en  to  en*,  then 
the  value  of  the  captured  charge  et  is 

ei=en>-en=~(v'2-v2)  ...........  (10) 

and  since  ^—  is  a  constant  for  this  drop,  any  charge 
rVi 

which  it  may  capture  will  always  be  proportional  to 


ATOMIC  NATURE  OF  ELECTRICITY 


69 


(v'2—v2),  that  is,  to  the  change  produced  in  the  velocity 
in  the  field  F  by  the  captured  ion.  The  successive  values 
of  v2  and  of  (v2—v2)  are  shown  in  Table  V. 

TABLE  V 


"=.04196 
12.45 


--=.02390 


2i-5 

•5222 

34-7 

•5222 

85-o 

•5222 

34-7 

•  5222 

16.  o 

•5222 
34-7 

•5222 
21.85 


=  •01505 


= .006144 


=  •01505 


= .03264 


=  .01505 


02390 


018064-2=  .00903 


.0088  5-7-1=.  0088  5 


.008914-1=  .00891 


.008914-1=  .00891 


.017594-2=  .  00880 


.017594-2=  .00880 


.00891 


00891 


It  will  be  seen  from  the  last  column  that  within  the 
limits  of  error  of  a,  stop-watch  measurement,  all  the 
charges  captured  have  exactly  the  same  value  save  in 
three  cases.  In  all  of  these  three  the  captured  charges 
were  just  twice  as  large  as  those  appearing  in  the  other 
changes.  Relationships  of  exactly  this  sort  have  been 
found  to  hold  absolutely  without  exception,  no  matter 
in  what  gas  the  drops  have  been  suspended  or  what  sort 
of  droplets  were  used  upon  which  to  catch  the  ions.  In 
many  cases  a  given  drop  has  been  held  under  observation 


70  THE  ELECTRON 

for  five  or  six  hours  at  a  time  and  has  been  seen  to 
catch  not  eight  or  ten  ions,  as  in  the  above  experiment, 
but  hundreds  of  them.  Indeed,  I  have  observed,  all 
told,  the  capture  of  many  thousands  of  ions  in  this  way, 
and  in  no  case  have  I  ever  found  one  the  charge  of  which, 
when  tested  as  above,  did  not  have  either  exactly  the 
value  of  the  smallest  charge  ever  captured  or  else  a  very 
small  multiple  of  that  value.  Here,  then,  is  direct,  unim- 
peachable proof  that  the  electron  is  not  a  "statistical  mean,''' 
but  that  rather  the  electrical  charges  found  on  ions  all  have 
either  exactly  the  same  value  or  else  small  exact  multiples  of 
that  value. 

H.   PROOF  THAT  ALL  STATIC  CHARGES  BOTH  ON  CON- 
DUCTORS AND  INSULATORS  ARE  BUILT  UP  OF 
ELECTRONS 

The  foregoing  experiment  leads,  however,  to  results 
of  much  more  fundamental  importance  than  that  men- 
tioned in  the  preceding  section.  The  charge  which  the 
droplet  had  when  it  first  came  under  observation  had 
been  acquired,  not  by  the  capture  of  ions  from  the  air, 
but  by  the  ordinary  frictional  process  involved  in  blow- 
ing the  spray.  If  then  ordinary  static  charges  are  built 
up  of  electrons,  this  charge  should  be  found  to  be  an 
exact  multiple  of  the  ionic  charge  which  had  been  found 
from  the  most  reliable  measurement  shown  in  Table  V 
to  be  proportional  to  the  velocity  .00891.  This  initial 
charge  en  on  the  drop  is  seen  from  equations  (9)  and  (10) 
to  bear  the  same  relation  to  (vl-}-v2)  which  the  ionic 
charge^'— en bears  to  (v'2—v2).  Now,  v^=  .5222/13.595 
=  .03842,  hence  vl-\-v2  =  .03842+. 04196=  .08038.  Di- 
viding this  by  9  we  obtain  .  00893 r  >  which  is  within  about 


ATOMIC  NATURE  OF  ELECTRICITY  71 

one-fifth  of  i  per  cent  of  the  value  found  in  the  last 
column  of  Table  V  as  the  smallest  charge  carried  by  an 
ion.  Our  experiment  has  then  given  us  for  the  first  time 
a  means  of  comparing  a  frictional  charge  with  the  ionic 
charge,  and  the  frictional  charge  has  in  this  instance  been 
found  to  contain  exactly  9  electrons.  A  more  exact  means 
of  making  this  comparison  will  be  given  presently,  but 
suffice  it  to  say  here  that  experiments  like  the  foregoing 
have  now  been  tried  on  thousands  of  drops  in  different 
media,  some  of  the  drops  being  made  of  non-conductors 
like  oil,  some  of  semi-conductors  like  glycerin,  some  of 
excellent  metallic  conductors  like  mercury.  In  every 
case,  without  a  single  exception,  the  initial  charge  placed 
upon  the  drop  by  the  frictional  process,  and  all  of  the 
dozen  or  more  charges  which  have  resulted  from  the 
capture  by  the  drop  of  a  larger  or  smaller  number  of 
ions,  have  been  found  to  be  exact  multiples  of  the  small- 
est charge  caught  from  the  air.  Some  of  these  drops 
have  started  with  no  charge  at  all,  and  one,  two,  three, 
four,  five,  and  six  elementary  charges  or  electrons  have 
been  picked  up.  Others  have  started  with  seven  or 
eight  units,  others  with  twenty,  others  with  fifty,  others 
with  a  hundred,  others  with  a  hundred  and  fifty  elemen- 
tary units,  and  have  picked  up  in  each  case  a  dozen  or 
two  of  elementary  charges  on  either  side  of  the  starting- 
point,  so  that  in  all  drops  containing  every  possible  num- 
ber of  electrons  between  one  and  one  hundred  and  fifty 
have  been  observed  and  the  number  of  electrons  which 
each  drop  carried  has  been  accurately  counted  by  the 
method  described.  When  the  number  is  less  than  fifty 
there  is  not  a  whit  more  uncertainty  about  this  count 
than  there  is  in  counting  one's  own  fingers  and  toes.  It 


72  THE  ELECTRON 

is  not  found  possible  to  determine  with  certainty  the 
number  of  electrons  in  a  charge  containing  more  than 
one  hundred  or  two  hundred  of  them,  for  the  simple 
reason  that  the  method  of  measurement  used  fails  to 
detect  the  difference  between  200  and  201,  that  is,  we 
cannot  measure  v'2—va  with  an  accuracy  greater  than 
one-half  of  i  per  cent.  But  it  is  quite  inconceivable  that 
large  charges  such  as  are  dealt  with  in  commercial  appli- 
cations of  electricity  can  be  built  up  in  an  essentially 
different  way  from  that  in  which  the  small  charges  whose 
electrons  we  are  able  to  count  are  found  to  be.  Further- 
more, since  it  has  been  definitely  proved  that  an  electrical 
current  is  nothing  but  the  motion  of  an  electrical  charge 
over  or  through  a  conductor,  it  is  evident  that  the 
experiments  under  consideration  furnish  not  only  the 
most  direct  and  convincing  of  evidence  that  all  electrical 
charges  are  built  up  out  of  these  very  units  which  we 
have  been  dealing  with  as  individuals  in  these  experi- 
ments, but  that  all  electrical  currents  consist  merely  in 
the  transport  of  these  electrons  through  the  conducting 
bodies. 

In  order  to  show  the  beauty  and  precision  with  which 
these  multiple  relationships  stand  out  in  all  experiments 
of  this  kind,  a  table  corresponding  to  much  more  precise 
measurements  than  those  given  heretofore  is  here  intro- 
duced (Table  VI).  The  time  of  fall  and  rise  shown  in 
the  first  and  second  columns  were  taken  with  'a  Hipp 
chronoscope  reading  to  one- thousandths  of  a  second. 
The  third  column  gives  the  reciprocals  of  these  times. 
These  are  used  in  place  of  the  velocities  v2  in  the  field, 
since  distance  of  fall  and  rise  is  always  the  same.  The 
fourth  column  gives  the  successive  changes  in  speed  due 


ATOMIC  NATURE  OF  ELECTRICITY 


73 


to  the  capture  of  ions.  These  also  are  expressed  merely 
as  time  reciprocals.  For  reasons  which  will  be  explained 
in  the  next  section,  each  one  of  these- changes  may  corre- 
spond to  the  capture  of  not  merely  one  but  of  several  dis- 
tinct ions.  The  numbers  in  the  fifth  column  represent 

TABLE  VI 


Sic. 

tp 
Sec. 

I 
tp 

(NJ 

»' 

i<£'£) 

(£+i) 

n 

&4) 

11.848 

80  .  708 

.01236  1 

.09655 

18 

005366 

11.890 

22.366 

•03234 

6 

005390 

11.908 

22.390 

.  04470 

.12887 

24 

005371 

11.904 

22.368 

03751 

7 

005358 

11.882 
i  i  .  906 
11.838 

140.565 
79  .  600 
34.748 

.007192!  ' 
-01254  /v 

•005348 
.Ol6l6 

i 
3 

005348 
005387 

.09138 
.09673 

17 
18 

-005375 
•005374 

11.816 

34.762 

.02870  ' 

.11289 

21 

.005376 

11.776 

34-846 

i  i  .  840 
r  i  .  904 

29.286 
29.236 

•03414  I 

.026872 

5 

005375 

.  H833 

22 

005379 

11.870 
11.952 

137.308 
34-638 

.007  268P 

.02884  K 

.021572 

4 

005393 

.09146 
-II303 

17 
21 

.005380 
.005382 

11.860 

,• 

.01623 

3 

.005410 

11.846 
ii  .912 

22.104\ 
22.268) 

.04507  i 

.04307 

8 

.005384 

.12926 

24 

.005386 

11.910 

500.  I 

.002000  ' 

.08619 

16 

•005387 

11.918 
11.870 
11.888 
11.894 
•11.878 

19.704! 

I9.668J 
77.630\ 
77.  806  / 
42.302 

•05079   1 

.01285   I 
.02364   / 

.04879 
•03874 
.OI079 

9 
7 

2 

.005421 
.005401 

,   .005395 

.13498 
.09704 
10783 

25 
18 

20 

•005399 

.005390 
.005392 

ii  880 

Means 

-005386 

- 

005384 

Duration  of  exp.   =45  min. 


Plate  distance 
Fall  distance 
Initial  volts 
Final  volts 

Temperature 


—  16  mm. 
=  10.21  mm. 
=  5,088.8 
=  5,081.2 

=  22.82°  C. 


Pressure 
Oil  density 
Air  viscosity 
Radius  (a) 


=  75.62  cm. 
=  .9199 
=  1,824X10  -i 
—  .000276  cm. 
=  •034 


£1=4.991X10 


Speed  of  fall        =  08584  cm./sec. 


simply  the  small  integer  by  which  it  is  found  that  the 
numbers  in  the  fourth  column  must  be  divided  in  order 
to  obtain  the  numbers  in  the  sixth  column.  These  will 
be  seen  to  be  exactly  alike  within  the  limits  of  error  of  the 
experiment.  The  mean  value  at  the  bottom  of  the  sixth 
column  represents,  then,  the  smallest  charge  ever  caught 


74 


THE  ELECTRON 


from  the  air,  that  is,  it  is  the  elementary  ionic  charge. 
The  seventh  column  gives  the  successive  values  of  vl-\-v2 
expressed  as  reciprocal  times.  These  numbers,  then,  rep- 
resent the  successive  values  of  the  total  charge  carried  by 
the  droplet.  The  eighth  column  gives  the  integers  by 
which  the  numbers  in  the  seventh  column  must  be 
divided  to  obtain  the  numbers  in  the  last  column.  These 
also  will  be  seen  to  be  invariable.  The  mean  at  the 
bottom  of  the  last  column  represents,  then,  the  electrical 
unit  out  of  which  the  frictional  charge  on  the  droplet  was 
built  up,  and  it  is  seen  to  be  identical  with  the  ionic  charge 
represented  by  the  number  at  the  bottom  of  the  sixth  column. 
It  may  be  of  interest  to  introduce  one  further  table 
(Table  VII)  arranged  in  a  slightly  different  way  to  show 

TABLE  VII 


n 

4.pi7X» 

Observed 
Charge 

» 

4.QI7XW 

Observed 
Charge 

I 

4  QI7 

IO 

40    1  7 

4Q   41 

2                     . 

0   834 

II    . 

1:4   OQ 

K3    OI 

lA.  7C 

12    

ZQ   OO 

CQ     12 

4 

IQ.66 

19  66 

I"?  .  . 

63    92 

63  68 

24.59 

24.  60 

14  

68.84 

68  65 

6 

20    ^O 

20   62 

ir 

737s; 

7 

34  42 

34  47 

16  

78  67 

78    34 

8        .  .  :     . 

•}Q    -24 

30  38 

17    . 

83  so 

83    22 

44   2"\ 

44  42 

18  

88.51 

how  infallibly  the  atomic  structure  of  electricity  follows 
from  experiments  like  those  under  consideration. 

In  this  table  4.917  is  merely  a  number  obtained 
precisely  as  above  from  the  change  in  speed  due  to  the 
capture  of  ions  and  one  which  is  proportional  in  this 
experiment  to  the  ionic  charge.  The  column  headed 
4.917X7*  contains  simply  the  whole  series  of  exact  mul- 


ATOMIC  NATURE  OF  ELECTRICITY  75 

tiples  of  this  number  from  i  to  18.  The  column  headed 
"  Observed  Charge  "  gives  the  successive  observed  values 
of  (»i+»a).  It  will  be  seen  that  during  the  time  of  obser- 
vation, about  four  hours,  this  drop  carried  all  possible 
multiples  of  the  elementary  charge  from  4  to  18,  save  only 
15.  No  more  exact  or  more  consistent  multiple  relationship 
is  found  in  the  data  which  chemists  have  amassed  on  the 
combining  powers  of  the  elements  and  on  which  the  atomic 
theory  of  matter  rests  than  is  found  in  the  foregoing  numbers. 
Such  tables  as  these — and  scores  of  them  could  be 
given — place  beyond  all  question  the  view  that  an 
electrical  charge  wherever  it  is  found,  whether  on  an 
insulator  or  a  conductor,  whether  in  electrolytes  or  in 
metals,  has  a  definite  granular  structure,  that  it  consists 
of  an  exact  number  of  specks  of  electricity  (electrons)  all 
exactly  alike,  which  in  static  phenomena  are  scat- 
tered over  the  surface  of  the  charged  body  and  in  current 
phenomena  are  drifting  along  the  conductor.  Instead 
of  giving  up,  as  Maxwell  thought  we  should  some  day  do, 
the  "  provisional  hypothesis  of  molecular  charges,"  we 
find  ourselves  obliged  to  make  all  our  interpretations  of 
electrical  phenomena,  metallic  as  well  as  electrolytic,  in 
terms  of  it. 

III.   MECHANISM  OF  CHANGE  OF  CHARGE  OF  A  DROP 

All  of  the  changes  of  charge  shown  in  Table  IV  were 
spontaneous  changes,  and  it  has  been  assumed  that  all 
of  these  changes  were  produced  by  the  capture  of  ions 
from  the  air.  When  a  negative  drop  suddenly  increases 
its  speed  in  the  field,  that  is,  takes  on  a  larger  charge  of 
its  own  kind  than  it  has  been  carrying,  there  seems  to  be 
no  other  conceivable  way  in  which  the  change  can  be 


76  THE  ELECTRON 

produced.  But  when  the  charge  suddenly  decreases  there 
is  no  a  priori  reason  for  thinking  that  the  change  may  not 
be  due  as  well  to  the  direct  loss  of  a  portion  of  the  charge 
as  to  the  neutralization  of  this  same  amount  of  electricity 
by  the  capture  of  a  charge  of  opposite  sign.  That,  how- 
ever, the  changes  do  actually  occur,  when  no  X-rays  or 
radioactive  rays  are  passing  between  the  plates,  only  by 
the  capture  of  ions  from  the  air,  was  rendered  probable  by 
the  fact  that  drops  not  too  heavily  charged  showed  the 
same  tendency  on  the  whole  to  increase  as  to  decrease  in 
charge.  This  should  not  have  been  the  case  if  there  were 
two  causes  tending  to  decrease  the  charge,  namely,  direct 
loss  and  the  capture  of  opposite  ions,  as  against  one  tend- 
ing to  increase  it,  namely,  capture  of  like  ions.  The 
matter  was  very  convincingly  settled,  however,  by  mak- 
ing observations  when  the  gas  pressures  were  as  low  as 
2  or  3  mm.  of  mercury.  Since  the  number  of  ions  present 
in  a  gas  is  in  general  directly  proportional  to  the  pressure, 
spontaneous  changes  in  charge  should  almost  never  occur 
at  these  low  pressures;  in  fact,  it  was  found  that  drops 
could  be  held  for  hours  at  a  time  without  changing.  The 
frequency  with  which  the  changes  occur  decreases  regu- 
larly with  the  pressure,  as  it  should  if  the  changes  are 
due  to  the  capture  of  ions.  For  the  number  of  ions 
formed  by  a  given  ionizing  agent  must  vary  directly  as 
the  pressure. 

Again,  the  changes  do  not,  in  general,  occur  when  the 
electrical  field  is  on,  for  then  the  ions  are  driven  instantly 
to  the  plates  as  soon  as  formed,  at  a  speed  of,  say, 
10,000  cm.  per  second,  and  so  do  not  have  any  oppor- 
tunity to  accumulate  in  the  space  between  them.  When 
the  field  is  off,  however,  they  do  so  accumulate,  until,  in 


ATOMIC  NATURE  OF  ELECTRICITY  77 

ordinary  air,  they  reach  the  number  of,  say,  20,000  per 
cubic  centimeter.  These  ions,  being  endowed  with  the 
kinetic  energy  of  agitation  characteristic  of  the  tempera- 
ture, wander  rapidly  through  the  gas  and  become  a  part 
of  the  drop  as  soon  as  they  impinge  upon  it.  It  was  thus 
that  all  the  changes  recorded  in  Table  IV  took  place. 

It  is  possible,  however,  so  to  control  the  changes  as 
to  place  electrons  of  just  such  sign  as  one  wishes,  and  of 
just  such  number  as  one  wishes,  within  limits,  upon  a 
given  drop.  If,  for  example,  it  is  desired  to  place  a  posi- 
tive electron  upon  a  given  drop  the  latter  is  held  with 
the  aid  of  the  field  fairly  close  to  the  negative  plate,  say 
the  upper  plate;  then  an  ionizing  agent- -X-rays  or 
radium—  is  arranged  to  produce  dniform  ionization  in 
the  gas  between  the  plates.  Since  now  all  the  positive 
ions  nibve  up  while  the  negatives  move  down,  the  drop 
is  in  a  shower  of  positive  ions,  and  if  the  ionization  is 
intense  enough  the  drop  is  sure  to  be  hit.  In  this  way 
a  positive  charge  of  almost  any  desired  strength  may  be 
placed  upon  the  drop. 

Similarly,  in  order  to  throw  a  negative  ion  or  ions 
upon  the  drop  it  is  held  by  the  field  close  to  the  lower, 
i.e.,  to  the  positive,  plate  in  a  shower  of  negative  ions 
produced  by  the  X-rays.  It  was  in  this  way  that  most 
of  the  changes  shown  in  Table  VI  were  brought  about. 
This  accounts  for  the  fact  that  they  correspond  in  some 
instances  to  the  capture  of  as  many  as  six  electrons. 

When  X-rays  are  allowed  to  fall  directly  upon  the 
drop  itself  the  change  in  charge  may  occur,  not  merely 
because  of  the  capture  of  ions,  but  also  because  the  rays 
eject  beta  particles,  i.e.,  negative  electrons,  from  the 
molecules  of  the  drop.  That  changes  in  charge  were 


78  THE  ELECTRON 

actually  produced  in  this  way  in  our  experiments  was 
proved  conclusively  in  1910  by  the  fact  that  when  the 
pressure  was  reduced  to  a  very  low  value  and  X-rays 
were  allowed  to  pass  through  the  air  containing  the  drop, 
the  latter  would  change  readily  in  the  direction  of  increas- 
ing positive  or  decreasing  negative  charge,  but  it  could 
almost  never  be  made  to  change  in  the  opposite  direc- 
tion. This  is  because  at  these  low  pressures  the  rays 
can  find  very  few  gas  molecules  to  ionize,  while  they 
detach  negative  electrons  from  the  drop  as  easily  as  at 
atmospheric  pressure.  This  experiment  proved  directly 
that  the  charge  carried  by  an  ion  in  gases  is  the  same  as  the 
charge  on  the  beta  or  cathode-ray  particle. 

When  it  was  desired  to  avoid  the  direct  loss  of  nega- 
tive electrons  by  the  drop,  we  arranged  lead  screens  so 
that  the  drop  itself  would  not  be  illuminated  by  the  rays, 
although  the  gas  underneath  it  was  ionized  by  them.1 

IV.      DIRECT   OBSERVATION   OF   THE   KINETIC   ENERGY    OF 
AGITATION  OF  A  MOLECULE 

I  have  already  remarked  that  when  a  drop  carries 
but  a  small  number  of  electrons  it  appears  to  catch  ions 
of  its  own  sign  as  rapidly  as  those  of  opposite  signs— a 
result  which  seems  strange  at  first,  since  the  ions  of 
opposite  sign  must  be  attracted,  while  those  of  like  sign 
must  be  repelled.  Whence,  then,  does  the  ion  obtain  the 
energy  which  enables  it  to  push  itself  up  against  this 
electrostatic  repulsion  and  attach  itself  to  a  drop  already 
strongly  charged  with  its  own  kind  of  electricity  ?  It 
cannot  obtain  it  from  the  field,  since  the  phenomenon  of 
capture  occurs  when  the  field  is  not  on.  It  cannot 

<  See  Phil.  Mag.,  XXI  (1911),  757. 


ATOMIC  NATURE  OF  ELECTRICITY  79 

obtain  it  from  any  explosive  process  which  frees. the  ion 
from  the  molecule  at  the  instant  of  ionization,  since 
in  this  case,  too,  ions  would  be  caught  as  well,  or 
nearly  as  well,  when  the  field  is  on  as  when  it  is  off.  Here, 
then,  is  an  absolutely  direct  proof  that  the  ion  must  be 
endowed  with  a  kinetic  energy  of  agitation  which  is 
sufficient  to  push  it  up  to  the  surface  of  the  drop  against 
the  electrostatic  repulsion  of  the  charge  on  the  drop. 

This  energy  may  easily  be  computed  as  follows :  Let 
us  take  a  drop,  such  as  was  used  in  one  of  these  experi- 
ments, of  radius  .000197  cm-  The  potential  at  the  sur- 
face of  a  charged  sphere  can  be  shown  to  be  the  charge 
divided  by  the  radius.  The  value  of  the  elementary 
electrical  charge  obtained  from  the  best  observations  of 
this  type,  is  4.774Xio~10  absolute  electrostatic  units. 
Hence  the  energy  required  to  drive  an  ion  carrying  the 
elementary  charge  e  up  to  the  surface  of  a  charged  sphere 
of  radius  r,  carrying  16  elementary  charges,  is 

i6X(4.774Xio-10)2 
—                           —  =i.95Xio~14  ergs. 
.000197  L— 


Now,  the  kinetic  energy  of  agitation  of  a  molecule  as 
deduced  from  the  value  of  e  herewith  obtained,  and  the 
kinetic  theory  equation,  p  =  ^nmc2,  is  5.75Xio~14  ergs. 
According  to  the  Maxwell-Boltzmann  Law  of  the  parti- 
tion of  energy,  which  certainly  holds  in  gases,  this  should 
also  be  the  kinetic  energy  of  agitation  of  an  ion.  It  will 
be  seen  that  the  value  of  this  energy  is  approximately 
three  times  that  required  to  push  a  single  ion  up  to  the 
surface  of  the  drop  in  question.  Hence  the  electrostatic 
forces  due  to  16  electrons  on  the  drop  are  too  weak  to 
exert  much  influence  upon  the  motion  of  an  approaching 


8o  THE  ELECTRON 

ion.  But  if  it  were  possible  to  load  up  a  drop  with 
negative  electricity  until  the  potential  energy  of  its 
charge  were  about  three  times  as  great  as  that  computed 
above  for  this  drop,  then  the  phenomenon  here  observed 
of  the  catching  of  new  negative  ions  by  such  a  negatively 
charged  drop  should  not  take  place,  save  in  the  excep- 
tional case  in  which  an  ion  might  acquire  an  energy 
of  agitation  considerably  larger  than  the  mean  value. 
Now,  as  a  matter  of  fact,  it  was  regularly  observed  that 
the  heavily  charged  drops  had  a  very  much  smaller  tend- 
ency to  pick  up  new  negative  ions  than  the  more  lightly 
charged  drops,  and,  in  one  instance,  we  watched  for  four 
hours  another  negatively  charged  drop  of  radius 
.000658  cm.,  which  carried  charges  varying  from  126  to 
150  elementary  units,  and  which  therefore  had  a  poten- 
tial energy  of  charge  (computed  as  above  on  the  assump- 
tion of  uniform  distribution)  varying  from  4.  6X  io~14  to 
5 . 47 X  io~14.  In  all  that  time  this  drop  picked  up  but  one 
single  negative  ion  when  the  field  was  off,  and  that 
despite  the  fact  that  the  ionization  was  several  times 
more  intense  than  in  the  case  of  the  drop  of  Table  I. 
Positive  ions  too  were  being  caught  at  almost  every  trip 
down  under  gravity.  (The  strong  negative  charge  on 
the  drop  was  maintained  by  forcing  on  negative  ions  by 
the  field  as  explained  above.) 

V.      POSITIVE  AND  NEGATIVE  ELECTRONS  EXACTLY  EQUAL 

The  idea  has  at  various  times  been  put  forth  in  con- 
nection with  attempts  to  explain  chemical  and  cohesive 
forces  from  the  standpoint  of  electrostatic  attractions 
that  the  positive  and  negative  charges  in  a  so-called 
neutral  atom  may  not  after  all  be  exactly  equal,  in  other 


ATOMIC  NATURE  OF  ELECTRICITY  8 1 

words,  that  there  is  really  no  such  thing  as  an  entirely 
neutral  atom  or  molecule.  As  a  matter  of  fact,  it  is 
difficult  to  find  decisive  tests  of  this'  hypothesis.  The 
present  experiments,  however,  make  possible  the  follow- 
ing sort  of  test.  I  loaded  a  given  drop  first  with  negative 
electrons  and  took  ten  or  twelve  observations  of  rise  and 
fall,  then  with  the  aid  of  X-rays,  by  the  method  indicated 
in  the  last  section,  I  reversed  the  sign  of  the  charge  on 
the  drop  and  took  a  corresponding  number  of  observa- 
tions of  rise  and  fall,  and  so  continued  observing  first  the 
value  of  the  negative  electron  and  then  that  of  the  posi- 
tive. Table  VIII  shows  a  set  of  such  observations  taken 
in  air  with  a  view  to  subjecting  this  point  to  as  rigorous  a 
test  as  possible.  Similar,  though  not  quite  so  elaborate, 
observations  have  been  made  in  hydrogen  with  the  same 
result.  The  table  shows  in  the  first  column  the  sign  of 
the  charge;  in  the  second  the  successive  values  of  the 
time  of  fall  under  gravity;  in  the  third  the  successive 
times  of  rise  in  the  field  F;  in  the  fourth  the  number  of 
electrons  carried  by  the  drop  for  each  value  of  //?;  and  in 
the  fifth  the  number,  characteristic  of  this  drop,  which 
is  proportional  to  the  charge  of  one  electron.  This  num- 
ber is  obtained  precisely  as  in  the  two  preceding  tables 
by  finding  the  greatest  common  divisor  of  the  successive 
values  of  (fli+fl2)  and  then  multiplying  this  by  an 
arbitrary  constant  which  has  nothing  to  do  with  the 
present  experiment  and  hence  need  not  concern  us  here 
(see  chap.  v). 

It  will  be  seen  that  though  the  times  of  fall  and  of 
rise,  even  when  the  same  number  of  electrons  is  carried 
by  the  drop,  change  a  trifle  because  of  a  very  slight 
evaporation  and  also  because  of  the  fall  in  the  potential 


THE  ELECTRON 
TABLE  VIII 


Sign  of  Drop 

4. 

*P 
Sec. 

n 

e 

63.118 

63  .  050 

63.186 

41.728! 

63.332 

41  •  590/ 

— 

62.328 

62.728 

25.740] 

^  =  6.713 

62.926 

25.798 

f  i 

62.900 

a 

63-214 

25io6J 

Mean=62.976 

63-538 

22.694! 

63.244 

22.830; 

12 

63.114 

25.870] 

63  .  242 

25.  876  [ 

II 

63.362 

25.484] 

+ 

63.136 
63.226 

10.830 
10.682 

^  =  6.692 

63  •  764 

10.756  > 

63.280 

10.778 

22 

63-530 

10.672 

63  .  268 

10.646 

63-642 

63  .  020 

71.664! 

62.820 

71-248; 

63-5I4 

52.668] 

-j- 

63.312 

52.800! 

63.776 

52  496] 

7 

61  =  6.702 

63.300 

52.860] 

63.156 

71.708 

6 

63.126 

Mean  =  63  .  407 

ATOMIC  NATURE  OF  ELECTRICITY 

TABLE  VIII— Continued 


Sign  of  Drop 

4 

*P 

Sec. 

w 

e 

63.228 
63  .  294 
63.184 

42.006 
41.920 

42.  1  08 

. 

8 

- 

63.  260 
63-478 
63  .  074 
63.306 

53-210 
52.922 
53  •  034 
53-438> 

1 

7 

ei  =  6.686 

63-414 
63-450 
63  -  446 
63-556 

12.888 
12.812 
12.748 
12.824 

iQ 

Mean  =  63.  335 

Duration  of  experiment  i  hr.  40  min.  Mean  £+  =  6.697 

Initial  volts  =1723.5  Mean  e  —  =  6 . 700 

Final  volts    =  1 702 .  i 
Pressure        =     53 ;  48  cm. 

of  the  battery,  yet  the  mean  value  of  the  positive  elec- 
tron, namely,  6.697,  agrees  with  the  mean  value  of  the 
negative  electron,  namely,  6 . 700,  or  to  within  less  than 
i  part  in  2,000.  Since  this  is  about  the  limit  of  the 
experimental  error  (the  probable  error  by  least  squares 
is  i  part  in  1,500),  we  may  with  certainty  conclude  that 
there  are  no  differences  of  more  than  this  amount  between 
the  values  of  the  positive  and  negative  electrons.  This  is 
the  best  evidence  I  am  aware  of  for  the  exact  neutrality 
of  the  ordinary  molecules  of  gases.  Such  neutrality,  if 
it  is  actually  exact,  would  seem  to  preclude  the  possi- 
bility of  explaining  gravitation  as  a  result  of  electrostatic 
forces  of  any  kind.  The  electromagnetic  effect  of  mov- 
ing charges  might,  however,  still  be  called  upon  for 
this  purpose. 


84  THE  ELECTRON 

VI.  RESISTANCE  OF  MEDIUM  TO  MOTION  OF  DROP  THROUGH 

IT  THE  SAME  WHEN  DROP  IS  CHARGED  AS  WHEN 

UNCHARGED 

A  second  and  equally  important  conclusion  can  be 
drawn  from  Table  VIII.  It  will  be  seen  from  the  column 
headed  "n"  that  during  the  whole  of  the  time  corre- 
sponding to  the  observations  in  the  third  group  from 
the  top  the  drop  carried  either  6  or  7  electrons,  while, 
during  the  last  half  of  the  time  corresponding  to  the 
observations  in  the  second  group  from  the  top,  it 
carried  three  times  as  many,  namely,  22  electrons. 
Yet  the  mean  times  of  fall  under  gravity  in  the  two 
groups  agree  to  within  about  one  part  in  one  thousand. 
The  time  of  fall  corresponding  to  the  heavier  charge 
happens  in  this  case  to  be  the  smaller  of  the  two. 
We  may  conclude,  therefore,  that  in  these  experiments  the 
resistance  which  the  medium  offers  to  the  motion  of  a  body 
through  it  is  not  sensibly  increased  when  the  body  becomes 
electrically  charged.  This  demonstrates  experimentally  the 
exact  validity  for  this  work  of  the  assumption  made  on 
p.  68  that  the  velocity  of  the  drop  is  strictly  propor- 
tional to  the  force  acting  upon  it,  whether  it  is  charged  or 
uncharged. 

The  result  is  at  first  somewhat  surprising  since, 
according  to  Sutherland's  theory  of  the  small  ion,  the 
small  mobility  or  diffusivity  of  charged  molecules,  as 
compared  with  uncharged,  is  due  to  the  additional  resist- 
ance which  the  medium  offers  to  the  motion  through  it 
of  a  charged  molecule.  This  additional  resistance  is 
due  to  the  fact  that  the  charge  on  a  molecule  drags 
into  collision  with  it  more  molecules  than  would  other- 
wise hit  it.  But  with  oil  drops  of  the  sizes  here  used 


ATOMIC  NATURE  OF  ELECTRICITY  85 

(a=5oXio~6)  the  total  number  of  molecular  collisions 
against  the  surface  of  the  drop  is  so  huge  that  even 
though  the  small  number  of  charges  on  it  might  produce 
a  few  more  collisions,  their  number  would  be  negligible 
in  comparison  with  the  total  number.  At  any  rate  the 
experiment  demonstrates  conclusively  that  the  charges 
on  our  oil  drops  do  not  influence  the  resistance  of  the 
medium  to  the  motion  of  the  drop.  This  conclusion 
might  also  have  been  drawn  from  the  data  contained  in 
Table  VI.  The  evidence  for  its  absolute  correctness  has 
been  made  more  convincing  still  by  a  comparison  of 
drops  which  carried  but  i  charge  and  those  which 
carried  as  many  as  68  unit  charges.  Further,  I  have 
observed  the  rate  of  fall  under  gravity  of  droplets 
which  were  completely  discharged,  and  in  every  case 
that  I  have  ever  tried  I  have  found  this  rate  pre- 
cisely the  same,  within  the  limits  of  error  of  the 
time  measurements,  as  when  it  carried  8  or  10  unit 
charges. 

VII.      DROPS   ACT   LIKE   RIGID    SPHERES 

It  was  of  very  great  importance  for  the  work,  an  ac- 
count of  which  will  be  given  in  the  next  chapter  to  deter- 
mine whether  the  drops  ever  suffer — either  because  of 
their  motion  through  a  resisting  medium,  or  because  of 
the  electrical  field  in  which  they  are  placed— any  appre- 
ciable distortion  from  the  spherical  form  which  a  freely 
suspended  liquid  drop  must  assume.  The  complete 
experimental  answer  to  this  query  is  contained  in  the 
agreement  of  the  means  at  the  bottom  of  the  last  and 
the  third  from  the  last  columns  in  Table  VI  and  in 
similar  agreements  shown  in  many  other  tables,  which 


86  THE  ELECTRON 

may  be  found  in  the  original  articles.1     Since  -  is  in  this 

i  g 

experiment  large  compared  to  — ,  the  value  of  the  greatest 

IF 

common  divisor  at  the  bottom  of  the  last  column  of 
Table  VI  is  determined  almost  wholly  by  the  rate  of  fall 
of  the  particle  under  gravity  when  there  is  no  field  at  all 
between  the  plates,  while  the  velocity  at  the  bottom  of 
the  third  from  the  last  column  is  a  difference  between  two 
velocities  in  a  strong  electrical  field.  If,  therefore,  the 
drop  were  distorted  by  the  electrical  field,  so  that  it 
exposed  a  larger  surface  to  the  resistance  of  the  medium 
than  when  it  had  the  spherical  form,  the  velocity  due  to 
a  given  force,  that  is,  the  velocity  given  at  the  bottom  of 
the  third  from  the  last  column,  would  be  less  than  that 
found  at  the  bottom  of  the  last  column,  which  corre- 
sponds to  motions  when  the  drop  certainly  was  spherical. 

Furthermore,  if  the  drops  were  distorted  by  their 
motion  through  the  medium,  then  this  distortion  would 
be  greater  for  high  speeds  than  for  low,  and  consequently 
the  numbers  in  the  third  from  the  last  column  would  be 
consistently  larger  for  high  speeds  than  for  low.  No 
such  variation  of  these  numbers  with  speed  is  apparent 
either  in  Table  VI  or  in  other  similar  tables. 

We  have  then  in  the  exactness  and  invariableness  of 
the  multiple  relations  shown  by  successive  differences  in 
speed  and  the  successive  sums  of  the  speeds  in  the  third 
from  the  last  and  the  last  columns  of  Table  VI  complete 
experimental  proof  that  in  this  work  the  droplets  act 
under  all  circumstances  like  undeformed  spheres.  It  is 
of  interest  that  Professor  Hadamard,2  of  the  University  of 

1  Phys.  Rev.,  Series  i,  XXXII  (1911),  349;  Series  2,  II  (1913),  109. 

2  Comptes  r endus  (1911),  1735. 


ATOMIC  NATURE  OF  ELECTRICITY  87 

Paris,  and  Professor  Lunn,1  of  the  University  of  Chicago, 
have  both  shown  from  theoretical  considerations  that 
this  would  be  the  case  with  oil  drops  as  minute  as  those 
with  which  these  experiments  deal,  so  that  the  conclu- 
sion may  now  be  considered  as  very  firmly  established 
both  by  the  experimentalist  and  the  theorist. 

<  Phys.  Rev.,  XXXV  (1912),  227. 


CHAPTER  V 

THE  EXACT  EVALUATION  OF  e 
•I.      DISCOVERY  OF  THE  FAILURE   OF   STOKES's  LAW 

Although  complete  evidence  for  the  atomic  nature  of 
electricity  is  found  in  the  fact  that  all  of  the  charges 
which  can  be  placed  upon  a  body  as  measured  by  the 
sum  of  speeds  fli-f-z>2,  and  all  the  changes  of  charge  which 
this  body  can  undergo  as  measured  by  the  differences  of 
speed  (v'2— v2)  are  invariably  found  to  be  exact  multiples 
of  a  particular  speed,  yet  there  is  something  still  to  be 
desired  if  we  must  express  this  greatest  common  divisor 
of  all  the  observed  series  of  speeds  merely  as  a  velocity 
which  is  a  characteristic  constant  of  each  particular  drop 
but  which  varies  from  drop  to  drop.  We  ought  rather 
to  be  able  to  reduce  this  greatest  common  divisor  to 
electrical  terms  by  finding  the  proportionality  factor 
between  speed  and  charge,  and,  that  done,  we  should,  of 
course,  expect  to  find  that  the  charge  came  out  a  uni- 
versal constant  independent  of  the  size  or  kind  of  drop 
experimented  upon.  The  attempt  to  do  this  by  the 
method  which  I  had  used  in  the  case  of  the  water  drops 
(p.  53),  namely,  by  the  assumption  of  Stokes's  Law, 
heretofore  taken  for  granted  by  all  observers,  led  to  the 
interesting  discovery  that  this  law  is  not  valid.1  Accord- 

1  Cunningham  (Proc.  Roy.  Soc.,  LXXXIII  [1910],  357)  and  the 
author  came  independently  to  the  conclusion  as  to  the  invalidity  of 
Stokes's  Law,  he  from  theoretical  considerations  developed  at  about  the 
same  time,  I  from  my  experimental  work. 

88 


THE  EXACT  EVALUATION  OF  e  89 

ing  to  this  law  the  rate  of  fall  of  a  spherical  drop  under 
gravity,  namely,  vtj  is  given  by 

*  =  %£(*-  p)  .'  ..............  (n) 

9*7 

in  which  rj  is  the  viscosity  of  the  medium,  a  the  radius 
and  o-  the  density  of  the  drop,  and  p  the  density  of  the 
medium.  This  last  quantity  was  neglected  in  (6),  p.  53, 
because,  with  the  rough  measurements  there  possible,  it 
was  useless  to  take  it  into  account,  but  with  our  oil  drops 
in  dry  air  all  the  other  factors  could  be  found  with  great 
precision. 

When  we  assume  the  foregoing  equation  of  Stokes  and 
combine  it  with  equation  (5)  on  p.  53,  an  equation  whose 
exact  validity  was  proved  experimentally  in  the  last 
chapter,  we  obtain,  after  substitution  of  the  purely  geo- 
metrical relation  7^=4/3  a3  (<r—  p),  the  following  expres- 
sion for  the  charge  en  carried  by  a  drop  loaded  with  n 
electrons  which  we  will  assume  to  have  been  counted  by 
the  method  described: 

_4/9> 


According  to  this  equation  the  elementary  charge  e^ 
should  be  obtained  by  substituting  in  this  the  greatest 
common  divisor  of  all  the  observed  series  of  values  o'f 
(fli~H2)  or  of  (v'2—  v2).  Thus,  if  we  call  this  (0i+%)0,  we 
have 


But  when  this  equation  was  tested  out  upon  different 
drops,  although  it  yielded  perfectly  concordant  results 


go  THE  ELECTRON 

so  long  as  the  different  drops  all  fell  with  about  the  same 
speed,  when  drops  of  different  speeds,  and,  therefore,  of 
different  sizes,  were  used,  the  values  of  d  obtained  were 
consistently  larger  the  smaller  the  velocity  under  gravity. 
For  example,  d  for  one  drop  for  which  Vi=  .  01085  cm.  per 
second  came  out  5 . 49 X  io~10,  while  for  another  of  almost 
the  same  speed,  namely,  v^=  .01176,  it  came  out  5.482; 
but  for  two  drops  whose  speeds  were  five  times  as  large, 
namely,  .0536  and  .0553,  et  came  out  5.143  and  5.145, 
respectively.  This  could  mean  nothing  save  that 
Stokes's  Law  did  not  hold  for  drops  of  the  order  of  mag- 
nitude here  used,  something  like  a=  .0002  cm.  (see  Sec- 
tion IV  below),  and  it  was  surmised  that  the  reason  for 
its  failure  lay  in  the  fact  that  the  drops  were  so  small  that 
they  could  no  longer  be  thought  of  as  moving  through 
the  air  as  they  would  through  a  continuous  homogeneous 
medium,  which  was  the  situation  contemplated  in  the 
deduction  of  Stokes's  Law.  This  law  ought  to  begin  to 
fail  asfsoon  as  the  inhomogeneities  in  the  medium — i.e., 
the  distances  between  the  molecules — began  to  be  at  all 
comparable  with  the  dimensions  of  the  drop.  Further- 
more, it  is  easy  to  see  that  as  soon  as  the  holes  in  the  * 
medium  begin  to  be  comparable  with  the  size  of  the 
drop,  the  latter  must  begin  to  increase  its  speed,  for  it 
may  then  be  thought  of  as  beginning  to  reach  the  stage 
in  which  it  can  fall  freely  through  the  holes  in  the 
medium.  This  would  mean  that  the  observed  speed  of 
fall  would  be  more  and  more  in  excess  of  that  given  by 
Stokes's  Law  the  smaller  the  drop  became.  But  the 
apparent  value  of  the  electronic  charge,  namely,  e^  is 
seen  from  equation  (13)  to  vary  directly  with  the  speed 
fe+fl2)0  imparted  by  a  given  force.  Hence  e^  should 


I 
THE  EXACT  EVALUATION  OF  c  91 

come  out  larger  and  larger  the  smaller  the  radius  of  the 
drop,  that  is,  the  smaller  its  velocity  under  gravity.  Now, 
this  was  exactly  the  behavior  shown  consistently  by  all 
the  oil  drops  studied.  Hence  it  looked  as  though  we  had 
discovered,  not  merely  the  failure  of  Stokes Js  Law,  but 
also  the  line  of  approach  by  means  of  which  it  might  be 
corrected. 

In  order  to  be  certain  of  our  ground,  however,  we 
were  obliged  to  initiate  a  whole  series  of  new  and  some- 
what elaborate  experiments. 

These  consisted,  first,  in  finding  very  exactly  what 
is  the  coefficient  of  viscosity  of  air  under  conditions  in 
which  it  may  be  treated  as  a  homogeneous  medium,  and. 
second,  in  finding  the  limits  within  which  Stokes's  Law 
may  be  considered  valid. 

II.      THE   COEFFICIENT   OF   VISCOSITY   OF   AIR 

The  experiments  on  the  coefficient  of  viscosity  of 
air  were  carried  out  in  the  Ryerson  Laboratory  by 
Dr.  Lachen  Gilchrist,  now  of  Toronto  Unfversity,  and 
Dr.  I.  M.  Rapp,  now  of  the  University  of  Oklahoma. 
Dr.  Gilchrist  used  a  method1  which  was  in  many  respects 
new  and  which  may  fairly  be  said  to  be  freer  from  theo- 
retical uncertainties  than  any  method  which  has  ever 
been  used.  He  estimated  that  his  results  should  not  be 
in  error  by  more  than  .  T  or  .  2  of  i  per  cent.  Dr.  Rapp 
used  a  form  of  the  familiar  capillary- tube  method,  but 
under  conditions  which  seemed  to  adapt  it  better  to  an 
absolute  evaluation  of  rj  for  air  than  capillary-tube 
arrangements  have  ordinarily  been. 

hys.  Rev.,  I,  N.S.  (1913),  124. 


92  THE  ELECTRON 

These  two  men,  as  the  result  of  measurements  which 
were  in  progress  for  more  than  two  years,  obtained  final 
means  which  were  in  very  close  agreement  with  one 
another  as  well  as  with  the  most  careful  of  preceding 
determinations.  It  will  be  seen  from  Table  IX  that 

TABLE  IX 

*,  for  Air 

.00018227  Rapp,  Capillary-tube  method,  1913 
(Phys.  Rev.,  II,  363). 

.00018257  Gilchrist,  Constant  deflection  method, 
1913  (Phys.  Rev.,  I,  124). 

.00018229  Hogg,  Damping  of  oscillating  cylin- 
ders, 1905  (Proc.  Am.  Acad.,  XL,  6n). 

.00018258  Tomlinson,  Damping  of  Swinging  Pendu- 
lum, 1886  (Phil.  Trans.,  CLXXVII, 
767). 

.00018232  Grindley  and  Gibson,  Flow  through  pipe, 
1908  (Proc.  Roy.  Soc.,  LXXX,  114). 

Mean...     .00018240 

every  one  of  the  five  different  methods  which  have  been 
used  for  the  absolute  determination  of  77  for  air  leads  to 
a  value  that  differs  by  less  than  one  part  in  one  thousand 
from  the  following  mean  value,  1723=  .  00018240.  It  was 
concluded,  therefore,  that  we  could  depend  upon  the 
value  of  T}  for  the  viscosity  of  air  under  the  conditions  of 
our  experiment  to  at  least  one  part  in  one  thousand. 
Very  recently  Dr.  E.  Harrington1  has  improved  still 
further  the  apparatus  designed  by  Dr.  Gilchrist  and  the 
authcTr  and  has  made  with  it  in  the  Ryerson  Laboratory 
a  determination  of  77  which  is,  I  think,  altogether  unique 
in  its  reliability  and  precision.  I  give  to  it  alone  greater 

1  Phys.  Rev.,  December,  1916. 


THE  EXACT  EVALUATION  OF  e  93 

weight  than  to  all  the  other  work  of  the  past  fifty  years 
in  this  field  taken  together.     The  final  value  is 

7723  =.000182  2  6      ' 

and  the  error  can  scarcely  be  more  than  one  part  in  two 
thousand. 

III.      LIMITS  OF  VALIDITY  OF  STOKES's  LAW 

In  the  theoretical  derivation  of  Stokes's  Law  the 
following  five  assumptions  are  made:  (i)  that  the 
inhomogeneities  in  the  medium  are  small  in  comparison 
with  the  size  of  the  sphere;  (2)  that  the  sphere  falls  as 
it  would  in  a  medium  of  unlimited  extent;  (3)  that  the 
sphere  is  smooth  and  rigid;  (4)  that  there  is  no  slipping 
of  the  medium  over  the  surface  of  the  sphere;  (5)  that 
the  velocity  with  which  the  sphere  is  moving  is  so  small 
that  the  resistance  to  the  motion  is  all  due  to  the  vis- 
cosity of  the  medium  and  not  at  all  due  to  the  inertia 
of  such  portion  of  the  media  as  is  being  pushed  forward 
by  the  motion  of  the  sphere  through  it. 

If  these  conditions  were  all  realized  then  Stokes's 
Law  ought  to  hold.  Nevertheless,  there  existed  up  to 
the  year  1910  no  experimental  work  which  showed  that 
actual  experimental  results  may  be  accurately  predicted 
by  means  of  the  unmodified  law,  and  Dr.  H.  D.  Arnold 
accordingly  undertook  in  the  Ryerson  Laboratory  to  test 
how  accurately  the  rates  of  fall  of  minute  spheres  through 
water  and  alcohol  might  be  predicted  by  means  of  it. 

His  success  in  these  experiments  was  largely  due  to 
the  ingenuity  which  he  displayed  in  producing  accurately 
spherical  droplets  of  rose-metal.  This  metal  melts  at 
about  82°  C.  and  is  quite  fluid  at  the  temperature  of 


94  THE  ELECTRON 

boiling  water.  Dr.  Arnold  placed  some  of  this  metal  in 
a  glass  tube  drawn  to  form  a  capillary  at  one  end  and 
suspended  the  whole  of  the  capillary  tube  in  a  glass 
tube  some  70  cm.  long  and  3  cm.  in  diameter.  He  then 
filled  the  large  tube  with  water  and  applied  heat  in  such 
a  way  that  the  upper  end  was  kept  at  about  100°  C., 
while  the  lower  end  was  at  about  60°.  He  then  forced 
the  molten  metal,  by  means  of  compressed  air,  out 
through  the  capillary  into  the  hot  water.  It  settled  in 
the  form  of  spray,  the  drops  being  sufficiently  cooled  by 
the  time  they  reached  the  bottom  to  retain  their  spherical 
shape.  This  method  depends  for  its  success  on  the 
relatively  slow  motion  of  the  spheres  and  on  the  small 
temperature  gradient  of  the  water  through  which  they 
fall.  The  slow  and  uniform  cooling  tends  to  produce 
homogeneity  of  structure,  while  the  low  velocities  allow 
the  retention  of  very  accurately  spherical  shape.  In  this 
way  Dr.  Arnold  obtained  spheres  of  radii  from  .  002  cm.  to 
.1  cm.,  which,  when  examined  under  the  microscope,  were 
found  perfectly  spherical  and  practically  free  from  surface 
irregularities.  He  found  that  the  slowest  of  these  drops 
fell  in  liquids  with  a  speed  which  could  be  computed  from 
Stokes's  Law  with  an  accuracy  of  a  few  tenths  of  i  per 
cent,  and  he  determined  experimentally  the  limits  of 
speed  through  which  Stokes's  Law  was  valid. 

Of  the  five  assumptions  underlying  Stokes's  Law, 
the  first,  third,  and  fourth  were  altogether  satisfied  in 
Dr.  Arnold's  experiment.  The  second  assumption  he 
found  sufficiently  realized  in  the  case  of  the  very  small- 
est drops  which  he  used,  but  not  in  the  larger  ones.  The 
question,  however,  of  the  effect  of  the  walls  of  the  vessel 
upon  the  motion  of  drops  through  the  liquid  contained 


THE  EXACT  EVALUATION  OF  e  95 

in  the  vessel  had  been  previously  studied  with  great 
ability  by  Ladenburg,1  who,  in  working  with  an  exceed- 
ingly viscous  oil,  namely  Venice  turpentine,  obtained 
a  formula  by  which  the  effects  of  the  wall  on  the  motion 
might  be  eliminated.  If  the  medium  is  contained  in  a 
cylinder  of  circular  cross-section  of  radius  R  and  of 
length  L,  then,  according  to  Ladenburg,  the  simple 
Stokes  formula  should  be  modified  to  read 

2  ga2(<r-p) 


Arnold  found  that  this  formula  held  accurately  in  all  of 
his  experiments  in  which  the  walls  had  any  influence  on 
the  motion.  Thus  he  worked  under  conditions  under 
which  all  of  the  first  four  assumptions  underlying 
Stokes's  Law  were  taken  care  of.  This  made  it  possible 
for  him  to  show  that  the  law  held  rigorously  when  the 
fifth  assumption  was  realized,  and  also  to  find  by  experi- 
ment the  limits  within  which  this  last  assumption  might 
be  considered  as  valid.  Stokes  had  already  found  from 
theoretical  considerations2  that  the  law  would  not  hold 
unless  the  radius  of  the  sphere  were  small  in  comparison 

with  -- ,  in  which  p  is  the  density  of  the  medium,  rj  its 

viscosity,  and  v  the  velocity  of  the  sphere.  This  radius 
is  called  the  critical  radius.  But  it  was  not  known  how 
near  it  was  possible  to  approach  to  the  critical  radius. 
Arnold's  experiments  showed  that  the  inertia  of  the 
medium  has  no  appreciable  effect  upon  the  rate  of 

'  Ann.  der  Phys.,  XXII  (1907),  287;  XXIII  (190$),  447- 
2  Math,  and  Phys.  Papers,  III,  59. 


g6  THE  ELECTRON 

motion  of  a  sphere  so  long  as  the  radius  of  that  sphere 
is  less  than  .  6  of  the  critical  radius. 

Application  of  this  result  to  the  motion  of  our  oil 
drops  established  the  fact  that  even  the  very  fastest 
drops  which  we  ever  observed  fell  so  slowly  that  not 
even  a  minute  error  could  arise  because  of  the  inertia  of 
the  medium.  This  meant  that  the  fifth  condition  neces- 
sary to  the  application  of  Stokes's  Law  was  fulfilled. 
Furthermore,  our  drops  were  so  small  that  the  second 
condition  was  also  fulfilled,  as  was  shown  by  the  work  of 
both  Ladenburg  and  Arnold.  The  third  condition  was 
proved  in  the  last  chapter  to  be  satisfied  in  our  experi- 
ments. Since,  therefore,  Arnold's  work  had  shown  very 
accurately  that  Stokes's  Law  does  hold  when  all  of  the 
.five  conditions  are  fulfilled,  the  problem  of  finding  a 
formula  for  replacing  Stokes's  Law  in  the  case  of  our 
oil-drop  experiments  resolved  itself  into  finding  in  just 
what  way  the  failure  of  assumptions  i  and  4  affected  the 
motion  of  these  drops. 

IV.      CORRECTION   OF   STOKES'S   LAW  FOR   INHOMOGE- 
NEITIES   IN  THE   MEDIUM 

The  first  procedure  was  to  find  how  badly  Stokes's 
Law  failed  in  the  case  of  our  drops.  This  was  done  by 
plotting  the  apparent  value  of  the  electron  ex  against  the 
observed  speed  under  gravity.  This  gave  the  curve 
shown  in  Fig.  4,  which  shows  that  though  for  very  small 
speeds  £z  varies  rapidly  with  the  change  in  speed,  for 
speeds  larger  than  that  corresponding  to  the  abscissa 
marked  1,000  there  is  but  a  slight  dependence  of  et  on 
speed.  This  abscissa  corresponds  to  a  speed  of  .  i  cm. 
per  second.  We  may  then  conclude  that  for  drops  which 


THE  EXACT  EVALUATION  OF  * 


97 


are  large  enough  to  fall  at  a  rate  of  i  cm.  in  ten  seconds 
or  faster,  Stokes's  Law  needs  but  a  small  correction, 
because  of  the  inhomogeneity  of  the  air. 


To  find  an  exact  expression  for  this  correction  we  may 
proceed  as  follows:  The  average  distance  which  a  gas 
molecule  goes  between  two  collisions  with  its  neighbors, 
a  quantity  well  known  and  measured  with  some  approach 


98  THE  ELECTRON 

to  precision  in  physics  and  called  "the  mean  free  path" 
of  a  gas  molecule,  is  obviously  a  measure  of  the  size  of 
the  holes  in  a  gaseous  medium.  When  Stokes  's  Law 
begins  to  fail  as  the  size  of  the  drops  diminish,  it  must 
be  because  the  medium  ceases  to  be  homogeneous,  as 
looked  at  from  the  standpoint  of  the  drop,  and  this 
means  simply  that  the  radius  of  the  drop  has  begun  to 
be  comparable  with  the  mean  size  of  the  holes  —  -a  quan- 
tity which  we  have  decided  to  take  as  measured  by  the 
mean'  free  path  /.  The  increase  in  the  speed  of  fall  over 
that  given  by  Stokes's  Law,  when  this  point  is  reached, 

must  then  be  some  function  of  -.     In  other  words,  the 

correct  expression  for  the  speed  vx  of  a  drop  falling 
through  a  gas,  instead  of  being 


as  Arnold  showed  that  it  was  when  the  holes  were  neg- 
ligibly small  —  as  the  latter  are  when  the  drop  falls 
through  a  liquid  —  should  be  of  the  form 


If  we  were  in  complete  ignorance  of  the  form  of  the  func- 
tion /  we  could  still  express  it  in  terms  of  a  series  of 
undetermined  constants  A,  B,  C,  etc.,  thus 


and  so  long  as  the  departures  from  Stokes's  Law  were 
small  as  Fig.  4  showed  them  to  be  for  most  of  our  drops, 


THE  EXACT  EVALUATION  OF  e  99 

we  could  neglect  the  second-order  terms  in  -  and  have 
therefore 


Using  this  corrected  form  of  Stokes's  Law  to  combine 
with  (9)  (p.  68),  we  should  obviously  get  the  charge  en 
in  just  the  form  in  which  it  is  given  in  (13),  save  that 
wherever  a  velocity  appears  in  (13)  we  should  now  have 

v 
to  insert  in  place  of  this  velocity  L    And  since  the 

T.~\~A.~ 

a 

velocity  of  the  drop  appears  in  the  3/2  power  in  (13),  if 
we  denote  now  by  e  the  absolute  value  of  the  electron 
and  by  eI}  as  heretofore,  the  apparent  value  obtained 
from  the  assumption  of  Stokes's  Law,  that  is,  from  the 
use  of  (13),  we  obtain  at  once 

e=  ,     £l  ,.  .  .  ..(16) 


In  this  equation  ex  can  always  be  obtained  from  (13), 
while  /  is  a  known  constant,  but  e,  A,  and  a  are  all 
unknown.  If  a  can  be  found  our  observations  permit 
at  once  of  the  determination  of  both  e  and  A ,  as  will  be 
shown  in  detail  under  Section  VI  (see  p.  103). 

However,  the  possibility  of  determining  e  if  we  know 
a  can  be  seen  in  a  general  way  without  detailed  analysis. 
For  the  determination  of  the  radius  of  the  drop  is 
equivalent  to  finding  its  weight,  since  its  density  is 
known.  That  we  can  find  the  charge  on  the  drop  as 
soon  as  we  can  determine  its  weight  is  clear  from  the 
simple  consideration  that  the  velocity  under  gravity  is 
proportional  to  its  weight,  while  the  velocity  in  a  given 


ioo  THE  ELECTRON 

electrical  field  is  proportional  to  the  charge  which  it 
carries.  Since  we  measure  these  two  velocities  directly, 
we  can  obtain  either  the  weight,  if  we  know  the  charge, 
or  the  charge,  if  we  know  the  weight.  (See  equation  9, 
p.  67.) 

V.      WEIGHING   THE   DROPLET 

The  way  which  was  first  used  for  finding  the  weight 
of  the  drop  was  simply  to  solve  Stokes's  uncorrected 
equation  (n)  (p.  89)  for  a  in  the  case  of  each  drop. 
Since  the  curve  of  Fig.  4  shows  that  the  departures  from 
Stokes's  Law  are  small  except  for  the  extremely  slow 
drops,  and  since  a  appears  in  the  second  power  in  (n),  it 
is  clear  that,  if  we  leave  out  of  consideration  the  very 
slowest  drops,  (n)  must  give  us  very  nearly  the  correct 
values  of  a.  We  can  then  find  the  approximate  value 
of  A  by  the  method  of  the  next  section,  and  after  it  is 
found  we  can  solve  (15)  for  the  correct  value  of  a.  This 
is  a  method  of  successive  approximations  which  theo- 
retically yields  a  and  A  with  any  desired  degree  of  pre- 
cision. As  a  matter  of  fact  the  whole  correction  term, 

A  -  is  a  small  one,  so  that  it  is  never  necessary  to  make 

more  than  two  approximations  to  obtain  a  with  much 
more  precision  than  is  needed  for  the  exact  evaluation 
of  e. 

As  soon  as  e  was  fairly  accurately  known  it  became 
possible,  as  indicated  above,  to  make  a  direct  weighing 
of  extraordinarily  minute  bodies  with  great  certainty 
and  with  a  very  high  degree  of  precision.  For  we  have 
already  shown  experimentally  that  the  equation 


THE  EXACT  EVALUATION  OF  e  101 

is  a  correct  one  and  it  involves  no  assumption  whatever 
as  to  the  shape,  or  size,  or  material  of  the  particle.  If 
we  solve  this  equation  for  the  weight  mg  of  the  particle 
we  get 


In  this  equation  en  is  known  with  the  same  precision  as  e, 
for  we  have  learned  how  to  count  n.  It  will  presently  be 
shown  that  e  is  probably  now  known  with  an  accuracy 
of  one  part  in  a  thousand,  hence  mg  can  now  be  deter- 
mined with  the  same  accuracy  for  any  body  which  can 
be  charged  up  with  a  counted  number  n  of  electrons  and 
then  pulled  up  against  gravity  by  a  known  electrical 
field,  or,  if  preferred,  simply  balanced  against  gravity 
after  the  manner  used  in  the  water-drop  experiment  and 
also  in  part  of  the  oil-drop  work.1  This  device  is  simply 
an  electrical  balance  in  place  of  a  mechanical  one,  and  it 
will  weigh  accurately  and  easily  to  one  ten-billionth  of  a 
milligram. 

Fifty  years  ago  it  was  considered  the  triumph  of 
the  instrument-maker's  art  that  a  balance  had  been 
made  so  sensitive  that  one  could  weigh  a  piece  of 
paper,  then  write  his  name  with  a  hard  pencil  on  the 
paper  and  determine  the  difference  between  the  new 
weight  and  the  old  —  that  is,  the  weight  of  the  name. 
This  meant  determining  a  weight  as  small  as  one-tenth 
or  possibly  one-hundredth  of  a  milligram  (a  milligram  is 
about  1/30,000  of  an  ounce).  Some  five  years  ago 
Ramsay  and  Spencer,  in  London,  by  constructing  a 
balance  entirely  out  of  very  fine  quartz  fibers  and  placing 
it  in  a  vacuum,  succeeded  in  weighing  objects  as  small 

1  See  Phil.  Mag.,  XIX  (1860),  216;  XXI  (1862),  757. 


102  THE  ELECTRON 

as  one-millionth  of  a  milligram,  that  is,  they  pushed  the 
limit  of  the  weighable  down  about  ten  thousand  times. 
The  work  which  we  are  now  considering  pushed  it  down 
at  least  ten  thousand  times  farther  and  made  it  possible 
to  weigh  accurately  bodies  so  small  as  not  to  be  visible 
at  all  to  the  naked  eye.  For  it  is  only  necessary  to 
float  such  a  body  in  the  air,  render  it  visible  by  reflected 
light  in  an  ultra-microscope  arrangement  of  the  sort  we 
were  using,  charge  it  electrically  by  the  capture  of  ions, 
count  the  number  of  electrons  in  its  charge  by  the  method 
described,  and  then  vary  the  potential  applied  to  the 
plates  or  the  charge  on  the  body  until  its  weight  is  just 
balanced  by  the  upward  pull  of  the  field.  The  weight 
of  the  body  is  then  exactly  equal  to  the  product  of  the 
known  charge  by  the  strength  of  the  electric  field.  We 
made  all  of  our  weighings  of  our  drops  and  the  deter- 
mination of  their  radii  in  this  way  as  soon  as  we  had 
located  e  with  a  sufficient  degree  of  precision  to  warrant 
it,1  Indeed,  even  before  e  is\ery  accurately  known  it 
is  possible  to  use  such  a  balance  for  a  fairly  accurate 
evaluation  of  the  radius  of  a  spherical  drop.  For  when 
we  replace  m  in  (18)  by  4/^ma3(or—p)  and  solve  for  a 
we  obtain 


rg(<r— P) 

The  substitution  in  this  equation  of  an  approximately 
correct  value  of  e  yields  a  with  an  error  but  one-third  as 
great  as  that  contained  in  the  assumed  value  of  e,  for  a 
is  seen  from  this  equation  to  vary  as  the  cube  root  of  e. 
This  is  the  method  which,  in  view  of  the  accurate  evalua- 

1  Phys.  Rev.,  II  (1913),   117.     This  paper  was  read  before  the 
Deutsche  physikalische  Geseilschaft  in  Berlin  in  June,  1912. 


THE  EXACT  EVALUATION  OF  e  103 

tion  of  e,  it  is  now  desirable  to  use  for  the  determination 
of  the  weight  or  dimensions  of  any  minute  body,  for  the 
method  is  quite  independent  of  the  nature  of  the  body 
or  of  the  medium  in  which  it  is  immersed.  Indeed,  it 
constitutes  as  direct  and  certain  a  weighing  of  the  body 
as  though  it  were  weighed  on  a  mechanical  balance. 

VI.      THE  EVALUATION  OF  6  AND  A 
I 

With  e,.  and  -  known,  we  can  easily  determine  e  and 

d 

A  from  the  equation 


for  if  we  write  this  equation  in  the  form 

=  *i.  ..(20) 


and  then  plot  the  observed  values  of  e^  as  ordinates  and 
the  corresponding  values  of  -  as  abscissae  we  should  get 

a  straight  line,  provided  our  corrected  form  of  Stokes's 
Law  (15)  (p.  99)  is  adequate  for  the  correct  representa- 
tion of  the  phenomena  of  fall  of  the  droplets  within  the 

range  of  values  of  -  in  which  the  experiments  lie.     If  no 

such  linear  relation  is  found,  then  an  equation  of  the  form 
of  (15)  is  not  adequate  for  the  description  of  the  phe- 
nomena within  this  range.  As  a  matter  of  fact,  a  linear 
relation  was  found  to  exist  for  a  much  wider  range  of 

values  of  -  than  was  anticipated  would  be  the  case.    The 
a 


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THE  ELECTRON 


THE  EXACT  EVALUATION  OF  e 


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intercept  of  this  line  on  the  axis  of  ordinates,  that  is,  the 
value  of  0i  when  -=o  is  seen  from  (20)  to  be  e*,  and  we 

have  but  to  raise  this  to  the  3/2  power  to  obtain  the 
absolute  value  of  e.  Again,  A  is  seen  from  (20)  to  be 
merely  the  slope  of  this  line  divided  by  the  intercept  on 
the  es  axis. 

In  order  to  carry  this  work  out  experimentally  it  is 

necessary  to  vary  -  and  find  the  corresponding  values 

of  61.  This  can  be  done  in  two  ways.  First,  we  may 
hold  the  pressure  constant  and  choose  smaller  and 
smaller  drops  with  which  to  work,  or  we  may  work  with 
drops  of  much  the  same  size  but  vary  the  pressure  of 
the  gas  in  which  our  drops  are  suspended,  for  the  mean 
free  path  /  is  evidently  inversely  proportional  to  the 
pressure. 

Both  procedures  were  adopted,  and  it  was  found  that 
a  given  value  of  et  always  corresponded  to  a  given  value 

of  - ,  no  matter  whether  /  was  kept  constant  and  a 

reduced  to,  say,  one-tenth  of  its  first  value,  or  a  kept  about 
the  same  and  /  multiplied  tenfold.  The  result  of  one 
somewhat  elaborate  series  of  observations  which  was 
first  presented  before  the  Deutsche  physikalische  Gesell- 
schaft  in  June,  1912,  and  again  before  the  British  Asso- 
ciation at  Dundee  in  September,  191 2,1  is  shown  in 
Figs.  5  and  6.  The  numerical  data  from  which  these 
curves  are  plotted  are  given  fairly  fully  in  Table  IX. 
[t  will  be  seen  that  this  series  of  observations  embraces 
a  study  of  58  drops.  These  drops  represent  all  of  those 
studied  for  60  consecutive  days,  no  single  one  being 

Phys.  Rev.,  II  (1913),  136- 


THE  EXACT  EVALUATION  OF  e 


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THE  EXACT  EVALUATION  OF  e 


109 


omitted. 


They  represent  a  thirty-fold  variation  in  - 


(from  .016,  drop  No.  i,  to  .444,  drop  No.  58),  a  seven- 
teen-fold  variation  in  the  pressure  p  (from  4.46  cm., 
drop  No.  56,  to  76.27  cm.,  drop  No.  10),  a  twelvefold 
variation  in  a  (from  4.69Xio~5  cm.,  drop  No.  28,  to 
58.56Xio~5  cm.,  drop  No.  i),  and  a  variation  in  the 


FIG.  7 

number  of  free  electrons  carried  by  the  drop  from  i  on 
drop  No.  28  to  136  on  drop  No.  56. 

The  experimental  arrangements  are  shown  in  Fig.  7. 
The  brass  vessel  D  was  built  for  work  at  all  pressures  up 
to  15  atmospheres,  but  since  the  present  observations 
have  to  do  only  with  pressures  from  76  cm.  down,  these 
were  measured  with  a  very  carefully  made  mercury  ma- 
nometer m,  which  at  atmospheric  pressure  gave  precisely 


no  THE  ELECTRON 

the  same  reading  as  a  standard  barometer.  Complete 
stagnancy  of  the  air  between  the  condenser  plates  M 
and  N  was  attained,  first,  by  absorbing  all  of  the  heat 
rays  from  the  arc  A  by  means  of  a  water  cell  w,  80  cm. 
long,  and  a  cupric  chloride  cell  d,  and,  secondly,  by 
immersing  the  whole  vessel  D  in  a  constant  temperature 
bath  G  of  gas-engine  oil  (40  liters),  which  permitted,  in 
general,  fluctuations  of  not  more  than  .  02°  C.  during  an 
observation.  This,  constant-temperature  bath  was  found 
essential  if  such  consistency  of  measurement  as  is  shown 
here  was  to  be  obtained.  A  long  search  for  causes  of 
slight  irregularity  revealed  nothing  so  important  as  this, 
and  after  the  bath  was  installed  all  of  the  irregularities 
vanished.  The  atomizer  A  was  blown  by  means  of  a 
puff  of  carefully  dried  and  dust-free  air  introduced 
through  cock  e.  The  air  about  the  drop  p  was  ionized 
when  desired,  or  electrons  discharged  directly  from  the 
drop,  by  means  of  Rontgen  rays  from  X,  which  readily 
passed  through  the  glass  window  g.  To  the  three  win- 
dows g  (two  only  are  shown)  in  the  brass  vessel  D  corre- 
spond, of  course,  three  windows  in  the  ebonite  strip  c, 
which  encircles  the  condenser  plates  M  and  N.  Through 
the  third  of  these  windows,  set  at  an  angle  of  about  28° 
from  the  line  Xpa  and  in  the  same  horizontal  plane,  the 
oil  drop  is  observed  through  a  short-focus  telescope  hav- 
ing a  scale  in  the  eyepiece  to  make  possible  the  exact 
measurement  of  the  speeds  of  the  droplet-star. 

In  plotting  the  actual  observations  I  have  used  the 

reciprocal  of  the  pressure  -  in  place  of  /,  for  the  reason 
that  /  is  a  theoretical  quantity  which  is  necessarily  pro- 
portional to  -  ,  while  p  is  the  quantity  actually  measured. 


THE  EXACT  EVALUATION  OF  e    '  in 

This  amounts  to  writing  the  correction- term  to  Stokes's 

Law  in  the  form  (  H )  instead  of  in  the  form  i-\-A  -  and 

\       pa/  a 

considering  b  the  undetermined  constant  which  is  to  be 
evaluated,  as  was  A  before,  by  dividing  the  slope  of  our 
line  by  its  ^-intercept. 

Nevertheless,  in  view  of  the  greater  ease  of  visualiza- 
tion of  -  all  the  values  of  this  quantity  corresponding 
to  successive  values  of  —  are  given  in  Table  IX.  Fig.  5 
shows  the  graph  obtained  by  plotting  the  values  of  et 
against  —  for  the  first  51  drops  of  Table  IX,  and  Fig.  6 
shows  the  extension  of  this  graph  to  twice  as  large  values 

of  —  and  €i.     It  will  be  seen  that  there  is  not  the  slightest 
pa 

indication  of  a  departure  from  a  linear  relation  between 

e-i  and  -'-  up  to  the  value  —  =  620. 2,  which  corresponds 
pa  pa 

to  a  value  of  -  of  .4439  (see  drop  No.  58,  Table  IX). 

Furthermore,  the  scale  used  in  the  plotting  is  such  that 
a  point  which  is  one  division  above  or  below  the  line  in 
Fig.  5  represents  in  the  mean  an  error  of  2  in  700.  // 
will  be  seen  from  Figs.  5  and  6  thai  there  is  but  one  drop 
in  the  58  whose  departure  from  the  line  amounts  to  as 
much  as  o .  5  per  cent.  It  is  to  be  remarked,  too,  that  this 
is  not  a  selected  group  of  drops,  but  represents  all  of  the 
drops  experimented  upon  during  60  consecutive  days,  dur- 
ing which  time  the  apparatus  was  taken  down  several 
times  and  set  up  anew.  It  is  certain,  then,  that  an 
equation  of  the  form  (15)  holds  very  accurately  up  to 


112  THE  ELECTRON 

-  = .  4.     The  last  drop  of  Fig.  6  seems  to  indicate  the 

beginning  of  a  departure  from  this  linear  relationship. 
Since  such  departure  has  no  bearing  upon  the  evaluation 
of  e,  discussion  of  it  will  not  be  entered  into  here,  although 
it  is  a  matter  of  great  interest  for  the  molecular  theory. 
Attention  may  also  be  called  to  the  completeness  of 
the  answers  furnished  by  Figs.  5  and  6  to  the  question 
raised  in  chap,  iv  as  to  a  possible  dependence  of  the  drag 
which  the  medium  exerts  on  the  drop  upon  the  amount 
of  the  latter 's  charge;  also,  as  to  a  possible  variation  of 
the  density  of  the  drop  with  its  radius.  Thus  drops 

Nos.  27  and  28  have  practically  identical  values  of  — , 

but  while  No.  28  carries,  during  part  of  the  time,  but 
i  unit  of  charge  (see  Table  IX),  drop  No.  27  carries 
29  times  as  much  and  it  has  about  7  times  as  large  a 
diameter.  Now,  if  the  small  drop  were  denser  than  the 
large  one,  or  if  the  drag  of  the  medium  upon  the  heavily 
charged  drop  were  greater  than  its  drag  upon  the  one 
lightly  charged,  then  for  both  these  reasons  drop  No.  27 
would  move  more  slowly  relatively  to  drop  No.  28 
than  would  otherwise  be  the  case,  and  hence  et  for  drop 
No.  27  would  fall  below  e^  for  drop  No.  28.  Instead  of 
this  the  two  d  fall  so  nearly  together  that  it  is  impossible 
to  represent  them  on  the  present  scale  by  two  separate 
dots.  Drops  Nos.  52  and  56  furnish  an  even  more 
striking  confirmation  of  the  same  conclusion,  for  both 

/ 
drops  have  about  the  same  value  for  -  and  both  are 

exactly  on  the  line,  though  drop  No.  56  carries  at  one 
time  68  times  as  heavy  a  charge  as  drop  No.  52  and  has 
three  times  as  large  a  radius.  In  general,  the  fact  that 


THE  EXACT  EVALUATION  OF  e  113 

Figs.  5  and  6  show  no  tendency  whatever  on  the  part  of 
either  the  very  small  or  the  very  large  drops  to  fall  above 
or  below  the  line  is  experimental  proof  of  the  joint  cor- 
rectness of  the  assumptions  of  constancy  of  drop-density 
and  independence  of  drag  of  the  medium  on  the  charge 
on  the  drop. 

The  values  of  e}  and  b  obtained  graphically  from  the 
^-intercept  and  the  slope  in  Fig.  5  are  e!  =  6i.  i3Xio~8 
and  b=  .000625,  p  being  measured,  for  the  purposes  of 
Fig.  5  and  of  this  computation  in  centimeters  of  Hg  at 
23°  C.  and  a  being  measured  in  centimeters.  The  value 
of  A  in  equations  15  and  16  (p.  99)  corresponding  to  this 
value  of  b  is  .874. 

Instead,  however,  of  taking  the  result  of  this  graphical 
evaluation  of  e,  it  is  more  accurate  to  reduce  each  of  the 
observations  on  eT  to  e  by  means  of  the  foregoing  value 
of  b  and  the  equation 

.   b 


The  results  of  this  reduction  are  contained  in  the  last 
column  of  Table  IX.  These  results  illustrate  very 
clearly  the  sort  of  consistency  obtained  in  these  observa- 
tions. The  largest  departure  from  the  mean  value  found 
anywhere  in  the  table  amounts  to  0.5  per  cent  and  "the 
probable  error"  of  the  final  mean  value  computed  in  the 
usual  way  is  16  in  61,000. 

Instead,  however,  of  using  this  final  mean  value  as 
the  most  reliable  evaluation  of  e,  it  was  thought  prefer- 
able to  make  a  considerable  number  of  observations  at 
atmospheric  pressure  on  drops  small  enough  to  make  tg 
determinable  with  great  accuracy  and  yet  large  enough 
so  that  the  whole  correction  term  to  Stokes's  Law 


H4  THE  ELECTRON 

amounted  to  but  a  small  percentage,  since  in  this  case, 
even  though  there  might  be  a  considerable  error  in  the 
correction-term  constant  b,  such  error  would  influence 
the  final  value  of  e  by  an  inappreciable  amount.  The 
first  23  drops  of  Table  IX  represent  such  observations. 
It  will  be  seen  that  they  show  slightly  greater  consistency 
than  do  the  remaining  drops  in  the  table  and  that  the 
correction-term  reductions  for  these  drops  all  lie  between 
i .  3  per  cent  (drop  No.  i)  and  5 . 6  per  cent  (drop  No.  23) , 
so  that  even  though  b  were  in  error  by  as  much  as  3  per 
cent  (its  error  is  actually  not  more  than  i .  5  per  cent),  e 
would  be  influenced  by  that  fact  to  the  extent  of  but 
o.  i  per  cent.  The  mean  value  of  e*3  obtained  from  the 
first  23  drops  is  61 . 12X  io~8,  a  number  which  differs  by 
i  part  in  3,400  from  the  mean  obtained  from  all  the 
drops. 

When  correction  is  made  for  the  fact  that  the  num- 
bers in  Table  IX  were  obtained  on  the  basis  of  the 
assumption  77=. 0001825,  instead  of  77=. 0001824  (see 
Section  II),  which  was  the  value  of  7723  chosen  in  1913 
when  this  work  was  first  published,  the  final  mean  value 
of  e  obtained  from  the  first  23  drops  is  6i.o85Xio~8. 
This  corresponds  to 

e=4.774Xio~10  electrostatic  units. 

I  have  already  indicated  that  as  soon  as  e  is  known  it 
becomes  possible  to  find  with  the  same  precision  which 
has  been  attained  in  its  determination  the  exact  number 
of  molecules  in  a  given  weight  of  any  substance,  the 
absolute  weight  of  any. atom  or  molecule,  the  average 
kinetic  energy  of  agitation  of  an  atom  or  molecule  at 
any  temperature,  and  a  considerable  number  of  other 


THE  EXACT  EVALUATION  OF  e  115 

important  molecular  and  radioactive  constants.  In 
addition,  it  has  recently  been  found  that  practically  all 
of  the  important  radiation  constants  like  the  wave- 
lengths of  X-rays,  Planck's  h,  the  Stefan-Boltzmann 
constant  o-,  the  Wien  constant  c2)  etc:,  depend  for  their 
most  reliable  evaluation  upon  the  value  of  e.  In  a  word, 
e  is  increasingly  coming  to  be  regarded,  not  only  as  the 
most  fundamental  of  physical  or  chemical  constants,  but  also 
the  one  of  most  supreme  importance  for  the  solution  of  the 
numerical  problems  of  modern  physics.  It  seemed  worth 
while,  therefore,  to  drive  the  method  herewith  developed 
for  its  determination  to  the  limit  of  its  possible  precision. 
Accordingly,  I  built  two  years  ago  a  new  condenser 
having  surfaces  which  were  polished  optically  and  made 
flat  to  within  two  wave-lengths  of  sodium  light.  These 
were  22  cm.  in  diameter  and  were  separated  by  3  pieces 
of  echelon  plates,  14 . 91 74  mm.  thick,  and  all  having  opti- 
cally perfect  plane-parallel  surfaces.  The  dimensions  of 
the  condenser,  therefore,  no  longer  introduced  an  uncer 
tainty  of  more  than  about  i  part  in  10,000.  The  volts 
were  determined  after -each  reading  in  terms  of  a  Weston 
standard  cell  and  are  uncertain  by  no  more  than  i  part 
in  3,000.  The  times  were  obtained  from  an  exception- 
ally fine  printing  chronograph  built  by  William  Gaertner 
&  Co.  It  is  controlled  by  a  standard  astronomical 
clock  and  prints  directly  the  time  to  hundred ths  of  a 
second.  All  the  other  elements  of  the  problem  were 
looked  to  with  a  care  which  was  the  outgrowth  of  .five 
years  of  experience  with  measurements  of  this  kind. 
The  present  form  of  the  apparatus  is  shown  in  diagram 
in  Fig.  8,  and  in  Fig.  9  is  shown  a  photograph  taken 
before  the  enclosing  oil  tank  had  been  added.  This  work 


n6 


THE  ELECTRON 


THE  EXACT  EVALUATION  OF  e 


117 


n8  THE  ELECTRON 

was  concluded  in  August,  1916,  and  occupied  the  better 
part  of  two  years  of  time.  The  final  table  of  results  and 
the  corresponding  graph  are  given  in  Table  X  and  in 
Fig.  10.  The  final  value  of  e*  computed  on  the  basis 
7/23=  .0001824  is  seen  to  be  now  6i.i26Xio~8  instead 
of  61.085,  or  -°7  Per  cent  higher  than  the  value  found 
in  1913.  But  Dr.  Harrington's  new  value  of  rj23)  namely, 
.00018226,  is  more  reliable  than  the  old  value  and  is 
lower  than  it  by  .  07  per  cent.  Since  rj  appears  in  the 
first  power  in  e*,  it  will  be  seen  that  the  new  value1  of  e, 
determined  with  new  apparatus  and  with  a  completely 
new  determination  of  all  the  factors  involved,  comes  out 
to  the  fourth  place  exactly  the  same  as  the  value  pub- 
lished in  1913,  namely, 

e=4.774Xio~10  absolute  electrostatic  units. 

The  corresponding  values  of  b  and  A  are  now  .000617 
and  .863,  respectively. 

Since  the  value  of  the  Faraday  constant  has  now  been 
fixed  virtually  by  international  agreement2  at  9,650  abso- 
lute electromagnetic  units,  and  since  this  is  the  number  N 
of  molecules  in  a  gram  molecule  times  the  elementary 
electrical  charge,  we  have 


Although  the  probable  error  in  this  number  computed  by 
the  method  of  least  squares  from  Table  X  is  but  one  part 
in  4,000,  it  would  be  erroneous  to  infer  that  e  and  N  are 
now  known  with  that  degree  of  precision,  for  there  are 

'For  full  details  see  Millikan,  Phil.  Mag.,  June,  1917. 

2At.  wt.  of  Ag.  =  io7.88;   electrochem.  eq't.  of  Ag.=  0.01188. 


THE  EXACT  EVALUATION  OF  e 

four  constant  factors  entering  into  all  of  the  results  in 
Table  X  and  introducing  uncertainties  as  follows  :  The 
coefficient  of  viscosity  77  which  appears  in  the  3/2  power 
introduces  into  e  and  N  a  maximum  possible  uncertainty 
of  less  than  o.  i  per  cent,  say  0.07  per  cent.  The  cross- 
hair distance  which  is  uniformly  duplicatable  to  one 
part  in  two  thousand  appears  in  the  3/2  power  and 
introduces  an  uncertainty  of  no  more  than  0.07  per 
cent.  All  the  other  factors,  such  as  the  volts  and  the 
distance  between  the  condenser  plates,  introduce  errors 
which  are  negligible  in  comparison.  The  uncertainty  in 
e  and  A^  is  then  that  due  to  two  factors,  each  of  which 
introduces  a  maximum  possible  uncertainty  of  about 
0.07  per  cent.  Following  the  usual  procedure,  we  may 
estimate  the  uncertainty  in  e  and  N  as  the  square  root 
of  the  sum  of  the  squares  of  these  two  uncertainties, 
that  is,  as  about  one  part  in  1000.  We  have  then: 

6=4.  774=*=  .oosXio"10 


Perhaps  these  numbers  have  little  significance  to  the 
general  reader  who  is  familiar  with  no  electrical  units  save 
those  in  which  his  monthly  light  bills  are  rendered.  If 
these  latter  seem  excessive,  it  may  be  cheering  to  reflect 
that  the  number  of  electrons  contained  in  the  quantity  of 
electricity  which  courses  every  second  through  a  common 
sixteen-candle-power  electric-lamp  filament,  and  for 
which  we  pay  1/100,000  of  i  cent,  is  so  large  that  if  all 
the  two  and  one-half  million  inhabitants  of  Chicago  were 
to  begin  to  count  out  these  electrons  and  were  to  keep  on 
counting  them  out  each  at  the  rate  of  two  a  second,  and 
if  no  one  of  them  were  ever  to  stop  to  eat,  sleep,  or  die, 


I2O 


THE  ELECTRON 


*>  too  N-  M   Qi  O   1-1  >o«   HI  t^vo   M  O*  «~-  -*OO   O  « 


MO-*i^ro«^.(r>oiHO«*o  i-^oo 

WMIO<NOOC>HHIWI^I-IHO>  OVCO 
fOtorO^t*t>OiO»0»0  VOO   t-«  t^ 


ir^mfssf&SsHSHS!?! 


-i* 


^  t^»  ^O   OMWvOO\t^OO  ^O^O   Ot^-WMi-i 
10  vo\O  CO   O>  O   O   O  O   O   IOMD  \r>  Q   Q   Msocp   M 


r»CO    t^Tj-fOtOM    M    HI    top    lOCO    NTj-«MWXOVO<Op<OCO  O1^ 


tOOO 
CS  <M 
O  I^ 

o  o  i  o      o  o  !  o  o  o  o  o  o  o  o  o  o  o  o  o 


• 


Oi 
>O    < 


_  ro  rO  tO  CO  to 


THE  EXACT  EVALUATION  OF 


121 


122  THE  ELECTRON 

it  would  take  them  just  twenty  thousand  years  to  finish 
the  task. 

Let  us  now  review,  with  Figs.  5  and  10  before  us,  the 
essential  elements  in  the  measurement  of  e.  We  dis- 
cover, first,  that  electricity  is  atomic,  and  we  measure  the 
electron  in  terms  of  a  characteristic  speed  for  each  drop- 
let. To  reduce  these  speed  units  to  electrical  terms,  and 
thus  obtain  an  absolute  value  of  e,  it  is  necessary  to  know 
how  in  a  given  medium  and  in  a  given  field  the  speed  due 
to  a  given  charge  on  a  drop  is  related  to  the  size  of  the 
drop.  This  we  know  accurately  from  Stokes's  theory 
and  Arnold's  experiments  when  the  holes  in  the  medium, 

that  is,  when  the  values  of  -  are  negligibly  small,  but 

when  -  is  large  we  know  nothing  about  it.     Consequently 

there  is  but  one  possible  way  to  evaluate  e,  namely,  to  find 
experimentally  how  the  apparent  value  of  e,  namely,  et 

varies  with  -  or  —  ,  and  from  the  graph  of  this  relation  to 
*  i 

find  what  value  -Ci  approaches  as  -  or  —  approaches  zero. 

a      pa 

So  as  to  get  a  linear  relation  we  find  by  analysis  that  we 

must  ploj  e^  instead  of  el  against  -  or  — .     We  then  get 

a      pa 

e  from  the  intercept  of  an  experimentally  determined 
straight  line  on  the  y-axis  of  our  diagram.  This  whole 
procedure  amounts  simply  to  reducing  our  drop- 
velocities  to  what  they  would  be  if  the  pressure  were  so 

large  or  —  so  small  that  the  holes  in  the  medium  were  all 
pa 

closed  up.  For  this  case  and  for  this  case  alone  we  know 
both  from  Stokes 's  and  Arnold's  work  exactly  the  law  of 
motion  of  the  droplet. 


CHAPTER  VI 

THE  MECHANISM  OF  IONIZATION  OF  GASES  BY 
X-RAYS  AND  RADIUM, RAYS 

I.      EARLY  EVIDENCE 

Up  to  the  year  1908  the  only  experiments  which  threw 
any  light  whatever  upon  the  question  as  to  what  the  act 
of  ionization  of  a  gas  consists  in  were  those  performed 
by  Townsend1  in  1900.  He  had  concluded  from  the 
theory  given  on  p.  34  and  from  his  measurements  on  the 
diffusion  coefficients  and  the  mobilities  of  gaseous  ions 
that  both  positive  and  negative  ions  in  gases  carry  unit 
charges.  This  conclusion  was  drawn  from  the  fact  that 

the  value  of  ne  in  the  equation  ne—-j^  came  out  about 

i .  23  X  io10  electrostatic  units,  as  it  does  in  the  electrolysis 
of  hydrogen. 

In  1908,  however,  Townsend2  devised  a  method  of 

measuring  directly  the  ratio  j-:  and  revised  his  original 

conclusions.  His  method  consisted  essentially  in  driving 
ions  by  means  of  an  electric  field  from  the  region  between 
two  plates  A  and  B  (Fig.  n),  where  they  had  been  pro- 
duced by  the  direct  action  of  X-rays,  through  the  gauze 
in  B,  and  observing  what  fraction  of  these  ions  was  driven 
by  a  field  established  between  the  plates  B  and  C  to  the 
central  disk  D  and  what  fraction  drifted  by  virtue  of 
diffusion  to  the  guard-ring  C. 

1  Phil.  Trans.,  CXCIII  (1900),  129. 
3  Proc.  Roy.  Soc.,  LXXX  (1908),  207. 
123 


124  THE  ELECTRON 

By  this  method  Townsend  found  that  ne  for  the 
negative  ions  was  accurately  i.23Xio10,  but  for  the 
positive  ions  it  was  2.4iXio10.  From  these  results 
the  conclusion  was  drawn  that  in  X-ray  ionization  all  of 
the  positive  ions  are  bivalent,  i.e.,  presumably,  that  the 
act  of  ionization  by  X-rays  consists  in  the  detachment 
from  a  neutral  molecule  of  two  elementary  electrical 
charges. 

Townsend  accounted  for  the  fact  that  his  early  experi- 
ments had  not  shown  this  high  value  of  ne  for  the 
positive  ions  by  the  assumption  that  by  the  time  the 

A 


FIG. ii 

doubly  charged  positive  ions  in  these  experiments  had 
reached  the  tubes  in  which  D  was  measured,  most  of 
them  had  become  singly  charged  through  drawing  to 
themselves  the  singly  charged  negative  ions  with  which 
they  were  mixed.  This  hypothesis  found  some  justifica- 
tion in  the  fact  that  in  the  early  experiments  the  mean 
value  of  ne  for  the  positive  ions  had  indeed  come  out 
some  15  or  20  per  cent  higher  than  i.23Xio10 — a  dis- 
crepancy which  had  at  first  been  regarded  as  attributable 
to  experimental  errors,  and  which  in  fact  might  well  be 
attributed  to  such  errors  in  view  of  the  discordance 
between  the  observations  on  different  gases. 


MECHANISM  OF  IONIZATION  OF  GASES        125 

Franck  and  Westphal,1  however,  in  1909  redeter- 
mined  ne  by  a  slight  modification  of  Townsend's  original 
method,  measuring  both  v0  and  D  independently,  and 
not  only  found,  when  the  positive  and  negative  ions  are 
separated  by  means  of  an  electric  field  so  as  to  render 
impossible  such  recombination  as  Tpwnsend  suggested, 
that  D  was  of  exactly  the  same  value  as  when  they  were 
not  so  separated,  but  also  that  ne  for  the  positive  ions  pro- 
duced by  X-rays  was  but  i .  4X  io10  instead  of  2 . 41 X  io10. 
Since  this  was  in  fair  agreement  with  Townsend's  original 
mean,  the  authors  concluded  that  only  a  small  fraction— 
about  9  per  cent— of  the  positive  ions  formed  by  X-rays 
are  doubles,  or  other  multiples,  and  the  rest  singles.  In 
their  experiments  on  the  ionization  produced  by  a-rays, 
/3-rays,  and  7-rays,  they  found  no  evidence  for  the 
existence  of  doubly  charged  ions. 

In  summarizing,  then,  the  work  of  these  observers 
it  could  only  be  said  that,  although  both  Townsend  and 
Franck  and  Westphal  drew  the  conclusion  that  doubly 
charged  ions  exist  in  gases  ionized  by  X-rays,  there  were 
such  contradictions  and  uncertainties  in  their  work  as 
to  leave  the  question  unsettled.  In  gases  ionized  by 
other  agencies  than  X-rays  no  one  had  yet  found  any 
evidence  for  the  existence  of  ions  carrying  more  than  a 
single  charge. 

II.      OIL-DROP   EXPERIMENTS    ON   VALENCY   IN 
GASEOUS   IONIZATION 

The  oil-drop  method  is  capable  of  furnishing  a  direct 
and  unmistakable  answer  to  the  question  as  to  whether 
the  act  of  ionization  of  a  gas  by  X-rays  or  other  agencies 

1  Verh.  deutsch.  phys.  Ges.,  March  5,  1909. 


126  THE  ELECTRON* 

consists  in  the  detachment  of  one,  of  several,  or  of  many 
electrons  from  a  single  neutral  molecule.  For  it  makes 
it  possible  to  catch  the  residue  of  such  a  molecule  prac- 
tically at  the  instant  at  which  it  is  ionized  and  to  count 
directly  the  number  of  charges  carried  by  that  residue. 
The  initial  evidence  obtained  from  this  method  seemed 
to  favor  the  view  that  the  act  of  ionization  may  consist 
in  the  detachment  of  quite  a  number  of  electrons  from  a 
single  molecule,  for  it  was  not  infrequently  observed 
that  a  balanced  oil  drop  would  remain  for  several  seconds 
unchanged  in  charge  while  X-rays  were  passing  between 
the  plates,  and  would  then  suddenly .  assume  a  speed 
which  corresponded  to  a  change  of  quite  a  number  of 
electrons  in  its  charge. 

It  was  of  course  recognized  from  the  first,  however, 
that  it  is  very  difficult  to  distinguish  between  the  prac- 
tically simultaneous  advent  upon  a  drop  of  two  or  three 
separate  ions  and  the  advent  of  a  doubly  or  trebly 
charged  ion,  but  a  consideration  of  the  frequency  with 
which  ions  were  being  caught  in  the  experiments  under 
consideration,  a  change  occurring  only  once  in,  say,  10 
seconds,  seemed  at  first  to  render  it  improbable  that  the 
few  double,  or  treble,  or  quadruple  catches  observed  when 
the  field  was  on  could  represent  the  simultaneous  advent 
of  separate  ions.  It  was  obvious,  however,  that  the  ques- 
tion could  be  conclusively  settled  by  working  with 
smaller  and  smaller  drops.  For  the  proportion  of  double 
or  treble  to  single  catches  made  in  a  field  of  strength 
between  1,000  and  6,000  volts  per  centimeter  should  be 
independent  of  the  size  of  the  drops  if  the  doubles  are 
due  to  the  advent  of  doubly  charged  ions,  while  this 
proportion  should  decrease  with  the  square  of  the  radius 


MECHANISM  OF  IONIZATION  OF  GASES        127 

of  the  drop  if  the  doubles  are  due  to  the  simultaneous 
capture  of  separate  ions. 

Accordingly,  Mr.  Harvey  Fletcher  and  the  author,1 
suspended,  by  the  method  detailed  in  the  preceding 
chapter,  a  very  small  positively  charged  drop  in  the 
upper  part  of  the  field  between  M  and  N  (Fig.  12), 
adjusting  either  the  charge  upon  the  drop  or  the  field 
strength  until  the  drop  was  nearly  balanced.  We  then 
produced  beneath  the  drop  a  sheet  of  X-ray  ionization. 
With  the  arrangement  shown  in  the  figure,  in  which  M 


Edrtf\ 


FIG.  12 


and  N  are  the  plates  of  the  condenser  previously  de- 
scribed, and  L  and  Lf  are  thick  lead  screens,  the  positive 
ions-  are  thrown  practically  at  the  instant  of  formation 
to  the  upper  plate.  When  one  of  them  strikes  the  drop 
it  increases  the  positive  charge  upon  it,  and  the  amount 
of  the  charge  added  by  the  ion  to  the  drop  can  be  com- 
puted from  the  observed  change  in  the  speed  of  the  drop. 
For  the  sake  of  convenience  in  the  measurement  of 
successive  speeds  a  scale  containing  70  equal  divisions 
was  placed  in  the  eyepiece  of  the  observing  cathetometer 
telescope,  which  in  these  experiments  produced  a 

1  Phil.  Mag.,  XXIII  (1911),  753. 


128  THE  ELECTRON 

magnification  of  about  15  diameters.  The  method  of  pro- 
cedure was,  in  general,  first,  to  get  the  drop  nearly 
balanced  by  shaking  off  its  initial  charge  by  holding  a 
little  radium  near  the  observing  chamber,  then,  with  a 
switch,  to  throw  on  the  X-rays  until  a  sudden  start  in 
the  drop  revealed  the  fact  that  an  ion  had  been  caught, 
then  to  throw  off  the  rays  and  take  the  time  required 
for  it  to  move  over  10  divisions,  then  to  throw  on  the 
rays  until  another  sudden  quickening  in  speed  indicated 
the  capture  of  another  ion,  then  to  measure  this  speed 
and  to  proceed  in  this  way  without  throwing  off  the  field 
at  all  until  the  drop  got  too  close  to  the.upper  plate,  when 
the  rays  were  thrown  off  and  the  drop  allowed  to  fall 
under  gravity  to  the  desired  distance  from  the  upper 
plate.  In  order  to  remove  the  excess  of  positive  charge 
which  the  drop  now  had  because  of  its  recent  captures, 
some  radium  was  brought  near  the  chamber  and  the 
field  thrown  off  for  a  small  fraction  of  a  second.  As 
explained  in  preceding  chapters,  ions  are  caught  by  the 
drop  many  times  more  rapidly  when  the  field  is  off  than 
when  it  is  on.  Hence  it  was  in  general  an  easy  matter 
to  bring  the  positively  charged  drop  back  to  its  balanced 
condition,  or  indeed  to  any  one  of  the  small  number  of 
working  speeds  which  it  was  capable  of  having,  and  then 
to  repeat  the  series  of  catches  described  above.  In  this 
way  we  kept  the  same  drop  under  observation  for  hours 
at  a  time,  and  in  one  instance  we  recorded  100  successive 
captures  of  ions  by  a  given  drop,  and  determined  in  each 
case  whether  the  ion  captured  carried  a  single  or  a 
multiple  charge. 

The  process  of  making  this  determination  is  exceed- 
ingly simple  and  very  reliable.    For,  since  electricity  is 


MECHANISM  OF  IONIZATION  OF  GASES        129 

atomic  in  structure,  there  are  only,  for  example,  three 
possible  speeds  which  a  drop  can  have  when  it  carries 
i,  2,  or  3  elementary  charges,  and  it  is  a  perfectly  simple 
matter  to  adjust  conditions  so  that  these  speeds  are  of 
such  different  values  that  each  one  can  be  recognized 
unfailingly  even  without  a  stop-watch  measurement. 
Indeed,  the  fact  that  electricity  is  atomic  is  in  no  way 
more  beautifully  shown  than  by  the  way  in  which,  as 
reflected  in  Table  XI,  these  relatively  few  possible  work- 
ing speeds  recur.  After  all  the  possible  speeds  have 
been  located  it  is  only  necessary  to  see  whether  one  of 
them  is  ever  skipped  in  the  capture  of  a  new  ion  in 
order  to  know  whether  or  not  that  ion  was  a  double. 
Table  XI  represents  the  results  of  experiments  made 
with  very  hard  X-rays  produced  by  means  of  a  powerful 
1 2 -inch  Scheidel  coil,  a  mercury- jet  interrupter,  and  a 
Scheidel  tube  whose  equivalent  spark-length  was  about 
5  inches.  No  attempt  was  made  in  these  experiments  to 
make  precise  determinations  of  speed,  since  a  high  degree 
of  accuracy  of  measurement  was  not  necessary  for  the 
purpose  for  which  the  investigation  was  undertaken. 
Table  XI  is  a  good  illustration  of  the  character  of  the 
observations.  The  time  of  the  fall  under  gravity  recorded 
in  the  column  headed  '%"  varies  slightly,  both  because 
of  observational  errors  and  because  of  Brownian  move- 
ments. Under  the  column  headed  'V  are  recorded  the 
various  observed  values  of  the  times  of  rise  through  10 
divisions  of  the  scale  in  the  eyepiece.  A  star  (*)  after  an 
observation  in  this  column  signifies  that  the  drop  Was 
moving  with  gravity  instead  of  against  it.  The  pro- 
cedure was  in  general  to  start  with  the  drop  either 
altogether  neutral  (so  that  it  fell  when  the  field  was  on 


130 


THE  ELECTRON 


with  the  same  speed  as  when  the  field  was  off) ,  or  having 
one  single  positive  charge,  and  then  to  throw  on  positive 

TABLE  XI 

Plate  Distance  1.6  cm.     Distance  of  Fall  .0975  cm.    Volts  1,015. 
Temperature  23°  C.     Radius  of  Drop  .  000063  cm. 


fr 

If 

No.  of 
Charges  on 
Drop 

No.  of 
Charges  on 
Ion  Caught 

<« 

tp 

No.  of 

Charges  on 
Drop 

No.  of 

Charges  on 
Ion  Caught 

19.0 

IOO.O 

16.0 
8.0 

I  P 
2P 
3? 

IP 
IP 

2O.O 

IO.O* 
2O.O* 
IOO.O 

i  N 

0 

i  P 

P 
P 

N 

2O.O* 

0 

20.0 

16.0 
8.0 

2P 
3? 

I  P 

IOO.O 

16.0 

IP 
2p 

P 
P 
i  P 

8.0 

3? 

IOO.O 

i  P 

17.0 

8.2 

6.0 

2P 
3? 
4? 

I  P 
IP 
IP 

104.0 
15.0 
9.0 

i  P 
2P 
3? 

i  P 
i  P 

T    P 

6.0 

4? 

I    JL 

7-0* 

2  N 

T) 

7^o* 

iN 
2N 

I    if 

iN 

IO.O* 

2N 
i  N 

I    P 
I    P 

20.  O* 

o 

TJ 

21.0 

20.0* 

95-o 
16-5 
8.0 

o 
iP 
2P 
3? 

iP 
iP 
i  P 

T    P 

IOO.O 

15.5 

8.0 
6.0 

iP 
2P 
3? 
4P 

I  P 
iP 
I  P 
I  P 

6.0 

4? 

I    A 

IOO.O 

iP 

T    P 

IOO.O 

iP 

T    P 

16.5 

2P 

1     -L 

16.0 

2P 

1    A 
T) 

8-4 

3? 

I  r 

20.0* 

o 

I    P 

IOO.O 

i  P 

T    P 

20.  O 

106.0 
16.0 
8.4 

iP 
2P 
3? 

IP 
IP 

16.6 

8.8 
5-7' 

2  P 

11 

I    -t 
I    P 
IP 

IO.O* 

i  N 

i  P 

IOO.O 

* 

I  P 

i  N 

2O.  0* 
IOO.O 

16.0 

o 
iP 
2P 

IP 
i  P 

2O.  0* 
IO.O* 

20.  o* 

O 

iN 

0 

iN 
iP 

IOO.O 

i  P 

i  P 

44  catches,  all  singles 

16.0 

2P 

i  P 

8.0 

3? 

MECHANISM  OF  IONIZATION  OF  GASES        131 

charges  until  its  speed  came  to  the  6.0  second  value, 
then  to  make  it  neutral  again  with  the  aid  of  radium, 
and  to  begin  over  again. 

It  will  be  seen  from  Table  XI  that  in  4  cases  out  of  44 
we  caught  negatives,  although  it  would  appear  from  the 
arrangement  shown  in  Fig.  12  that  we  could  catch  only 
positives.  These  negatives  are  doubtless  due  to  second- 
ary rays  which  radiate  in  all  directions  from  the  air 
molecules  when  these  are  subjected  to  the  primary  X-ray 
radiation. 

Toward  the  end  of  Table  XI  is  an  interesting  series 
of  catches.  At  the  beginning  of  this  series,  the  drop 
was  charged  with  2  negatives  which  produced  a  speed 
in  the  direction  of  gravity  of  6 . 5  seconds.  It  caught  in 
succession  6  single  positives  before  the  field  was  thrown  off. 
The  corresponding  times  were  6.5*,  10*,  20*,  100,  15.5, 
8.0,  6.0.  The  mean  time  during  which  the  X-rays  had 
to  be  on  in  order  to  produce  a  " catch"  was  in  these 
experiments  about  six  seconds,  though  in  some  instances 
it  was  as  much  as  a  minute.  The  majority  of  the  times 
recorded  in  column  tp  were  actually  measured  with  a 
stop  watch  as  recorded,  but  since  there  could  be  no 
possibility  of  mistaking  the  ico-second  speed,  it  was 
observed  only  four  or  five  tirnes.  It  will  be  seen  from 
Table  XI  that  out  of  44  catches  of  ions  produced  by 
every  hard  X-ray  there  is  not  a  single  double.  As  a 
result  of  observing  from  500  to  i  ,000  catches  in  the  man- 
ner illustrated  in  Table  XI,  we  came  to  the  conclusion 
that,  although  we  had  entered  upon  the  investigation 
with  the  expectation  of  proving  the  existence  of  valency 
in  gaseous  ionization,  we  had  instead  obtained  direct, 
unmistakable  evidence  that  the  act  of  ionization  of  air 


132  THE  ELECTRON 

molecules  by  both  primary  and  secondary  X-rays  of  widely 
varying  degrees  of  hardness,  as  well  as  by  /3-  and  y-rays, 
uniformly  consists  ,  under  all  the  conditions  which  we  were 
able  to  investigate,  in  the  detachment  from  a  neutral  molecule 
of  one  single  elementary  electrical  charge. 

III.      RECENT    EVIDENCE    A$    TO    NATURE    OF    IONIZATION 
PRODUCED   BY   ETHER   WAVES 

Although  Townsend  and  Franck  and  Westphal  dis- 
sented from  the  foregoing  conclusion,  all  the  evidence 
which  has  appeared  since  has  tended  to  confirm  it.  Thus 
Salles,1  using  a  new  method  due  to  Langevin  of  measuring 


directly  the  ratio  f-^j  of  the  mobility  to  the  diffusion 

coefficient,  concluded  that  when  the  ionization  is  produced 
by  7-rays  there  are  no  ions  bearing  multiple  charges. 
Again,  the  very  remarkable  photographs  (see  plate 
opposite  p.  187)  taken  by  C.  T.  R.  Wilson  in  the 
Cavendish  Laboratory  of  the  tracks  made  by  the  passage 
of  X-rays  through  gases  show  no  indication  of  a  larger 
number  of  negatively  than  of  positively  charged  droplets. 
Such  an  excess  is  to  be  expected  if  the  act  of  ionization 
ever  consists  in  these  experiments  in  the  detachment  of 
two  or  more  negative  electrons  from  a  neutral  molecule. 
Further,  if  the  initial  act  of  ionization  by  X-rays  ever 
consists  in  the  ejection  of  two  or  more  corpuscles  from 
a  single  atom,  there  should  appear  in  these  Wilson  pho- 
tographs a  rosette  consisting  of  a  group  of  zigzag  lines 
starting  from  a  common  point.  A  glance  at  the  plate 
opposite  p.  189  shows  that  this  is  not  the  case,  each 
zigzag  line  having  its  own  individual  starting-point. 

1  Le  Radium,  X  (1913),  113,  119. 


MECHANISM  OF  IONIZATION  OF  GASES        133 

There  are  two  other  types  of  experiments  which 
throw  light  on  this  question. 

When  in  the  droplet  experiments  the  X-rays  are 
allowed  to  fall  directly  upon  the  droplet,  we  have  seen 
that  they  detach  negative  electrons  from  it,  and  if  the 
gas  is  at  so  low  a  pressure  that  there  is  very  little  chance 
of  the  capture  of  ions  by  the  droplet,  practically  all  of 
its  changes  in  charge  have  this  cause.  ' Changes  produced 
under  these  conditions  appear,  so  far  as  I  have  yet  been 
able  to  discover,  to  be  uniformly  unit  changes,  though 
I  have  not  yet  made  a  systematic  or  exhaustive  study  of 
this  point.  Also,  when  the  changes  are  produced  by  the 
incidence  on  the  droplet  of  ultra-violet  light,  so  far  as 
experiments  carried  out  in  the  Ryerson  Laboratory  go, 
they  usually,  though  not  always,  have  appeared  to  cor- 
respond to  the  loss  of  one  single  electron.  The  same 
seems  to  have  been  true  in  the  experiments  reported  by 
A.  Joffe,1  who  has  given  this  subject  careful  study. 
Meyer  and  Gerlach,  however,2  seem  very  often  to 
observe  changes  corresponding  to  the  simultaneous  loss 
of  several  electrons. 

It  is  to  be  noted,  however,  that  their  drops  are  gen- 
erally quite  heavily  charged,  carrying  from  10  to  30 
electrons.  Under  such  conditions  the  loss  of  a  single 
electron  makes  but  a  minute  change  in  speed,  and  is 
therefore  likely  not  only  to  be  unnoticed,  but  to  be  almost 
impossible  to  detect  until  the  change  has  become  more 
pronounced  through  the  loss  of  several  electrons.  This 
question,  then,  can  be  studied  reliably  only  when  the  field  is 
powerful  enough  to  hold  the  droplet  balanced  with  only  one 

1  Sitzungsber.  d.  k.  Bayerischen  Akad.  d.  Wiss.  (1913),  p.  19. 
Ann.  d.  Phys.,  XLV,  177;  XL VII,  227. 


134  THE  ELECTRON 

or  two  free  electrons  upon  it.  I  do  not  consider,  therefore, 
that  the  experiments  of  Meyer  and  Gerlach  contain  any 
evidence  that  the  act  of  ionization  by  ultra-violet  light 
detaches  more  than  one  electron  from  a  single  atom. 
Nor  indeed  do  they  claim  that  it  does,  while  the  evidence 
accumulated  in  the  Ryerson  Laboratory,  though  not  yet 
complete,  points  strongly  the  other  way. 

Table  XII  contains  one  series  of  observations  taken 
with  my  apparatus  by  Mr.  P.  I.  Pierson.  The  first 
column  gives  the  volts  applied  to  the  plates  of  the  con- 
denser shown  in  Fig.  7,  p.  109.  These  were  made  variable 
so  that  the  drop  might  always  be  pulled  up  with  a  slow 
speed  even  though  its  positive  charge  were  continually 
increasing.  The  second  and  third  columns  give  the  times 
required  to  move  i  cm.  under  gravity  and  under  the 
field  respectively.  The  fourth  column  gives  the  time 
intervals  required  for  the  drop  to  experience  a  change  in 
charge  under  the  influence  of  a  constant  source  of  ultra- 
violet light — a  quartz  mercury  lamp.  The  fifth  column 
gives  the  total  charge  carried  by  the  drop  computed  from 
equation  (12),  p.  89.  The  sixth  column  shows  the  change 
in  charge  computed  from  equation  (10),  p.  68.  This  is 
seen  to  be  as  nearly  a  constant  as  could  be  expected  in 
view  of  Brownian  movements  and  the  inexact  measure- 
ments of  volts  and  times.  The  mean  value  of  ^  is  seen 
to  be  5.  iXio~10  which  yields  with  the  aid  of  equation 
(16),  p.  99,  after  the  value  of  A  found  for  oil  drops  has 
been  inserted,  0  =  4. 77X10"",  which  is  in  better  agree- 
ment with  the  result  obtained  with  oil  drops  than  we 
had  any  right  to  expect.  In  these  experiments  the  light 
was  weak /so  that  the  changes  come  only  after  an  average 
interval  of  29  seconds  and  it  will  be  seen  that  they  are  all 


MECHANISM  OF  IONIZATION  OF  GASES        135 


unit  changes.     When  the  light  was  more  intense  we 
sometimes  appeared  to  get  double  and  in  one  case  treble 

TABLE  XII 

MERCURY  DROPLET  OF  RADIUS  o  =  8Xio-s  CM.  DISCHARGING  ELEC- 
TRONS UNDER  THE  INFLUENCE  OF  ULTRA- VlOLET   LlGHT 


Volts 

Drop  No.  i 
Per  Cm. 

tp  Sec. 
per  Cm. 

Time  Interval 
between 
Discharges 
in  Seconds 

«nXio« 

Change 
in  c 

Change 
in  n 

2,260  
-i  070 

II.  O 

no 

—  I2OO 
-4-      32  8 

\ 

49-4 

CQ   ir 

I 

1,  060.  . 

II   O 

—    IQ4 

II 

"?4.4 

4-4 

I 

I  060 

~\~    IQO 

12.8 

60  8 

6  4 

I 

1,820  
I  600 

II.  2 

+    22O 
+    23O 

23 

40 

65.0 
60  8 

4-2 

4  8 

I 

I 

I,  ceo.  . 

+    332 

15.2 

7^.  i 

c.3 

I 

3,040  

2   CAO 

Drop  No.  i 
10.4 

+      98 
+    2OO 

5-6 

43-5 

4.0  4. 

t     Q 

I 

2,230.  . 

+    3OO 

18.6 

ct    2 

5-8 

I 

2,230.  . 

+    76 

3-5-0 

60.7 

5-5 

I 

1,030.  . 

-1-  200 

42 

6e;  o 

4   3 

I 

1,810  

+  176 

54 

69.6 

4-6 

I 

i,6co.  . 

' 

+  2  <?o 

70 

7C    2 

5-6 

I 

1,520  

4-  soo 

45 

70.4 

4-2 

I 

I.C2O.  . 

no 

9-8 

85  i 

e.  c 

I 

Mean.  . 

29 

Mean.  . 

S-i 

changes,  but  since  these  uniformly  appear  with  less  and 
less  frequency  both  as  the  charge  diminishes  and  as  the 


136  THE  ELECTRON 

interval  between  the  changes  is  made  larger,  the  inference 
is  inevitable  that  when  multiple  changes  appear  fre- 
quently, as  they  do  in  Meyer  and  Gerlach's  work,  it  is 
because  some  of  the  changes  in  speed  escape  the  notice 
of  the  observer. 

So  long,  then,  as  we  are  considering  the  ionization  of 
neutral  atoms  through  the  absorption  of  an  ether  wave 
of  any  kind,  the  evidence  at  present  available  indicates 
that  the  act  always  consists  in  the  detachment  from  the 
atom  of  one  single  negative  electron,  the  energy  with 
which  this  electron  is  ejected  from  the  atom  depending,  as 
we  shall  see  in  chap,  x,  in  a  very  definite  and  simple  way 
upon  the  frequency  of  the  ether  wave  which. ejects  it. 

IV.      IONIZATION   BY  /3-RAYS 

When  the  ionization  is  due  to  the  passage  of  /3-rays 
through  matter,  the  evidence  of  the  oil-drop  experiments 
as  well  as  that  of  C.  T.  R.  Wilson's  experiments  (see 
chap.  IX)  on  the  photographing  of  the  tracks  of  the 
/3-rays  is  that  here,  too,  the  act  consists  in  the  detachment 
of  one  single  electron  from  a  single  atom.  This  experi- 
mental result  is  easy  to  understand  in  the  case  of  the 
/3-rays,  when  it  is  remembered  that  Wilson's  photo- 
graphs prove  directly  the  fact,  long  known  from  other 
types  of  evidence,  that  a  /3-ray,  in  general,  ionizes  but  a 
very  minute  fraction  of  the  number  of  atoms  through 
which  it  shoots  before  its  energy  is  expended.  If,  then, 
its  chance,  in  shooting  through  an  atom,  of  coming  near 
enough  to  one  of  the  electronic  constituents  of  that  atom 
to  knock  it  out  is  only  one  in  one  thousand,  or  one  in 
one  million,  then  its  chance  of  getting  near  enough  to 
two  electronic  constituents  of  the  same  atom  to  knock 


MECHANISM  OF  IONIZATION  OF  GASES        137 

them  both  out  is  likely  to  be  negligibly  small.  The 
argument  here  rests,  however,  on  the  assumption  that 
the  corpuscles  within  the  atom  are  independent  of  one 
another,  which  is  not  necessarily  the  case,  so  that  the 
matter  must  be  decided  after  all  solely  by  experiment. 
The  difference  between  the  act  of  ionization  when 
produced  by  a  /3-ray  and  when  produced  by  an  ether 
wave  seems,  then,  to  consist  wholly  in  the  difference  in 
the  energy  with  which  the  two  agencies  hurl  the  electron 
from  its  mother  atom.  Wilson's  photographs  show  that 
0-rays  do  not  eject  electrons  from  atoms  with  appre- 
ciable speeds^  while  ether  waves  may  eject  them  with 
tremendous  energy.  Some  of  Wilson's  photographs 
showing  the  effect  of  passing  X-rays  through  air  are 
shown  in  the  most  interesting  plate  opposite  p.  189. 
The  original  X-rays  have  ejected  electrons  with  great 
speeds  from  a  certain  few  of  the  atoms  of  the  gas, 
and  it  is  the  tracks  of  these  electrons  as  they  shoot 
through  the  atoms  of  the  gas,  ionizing  here  and  there  as 
they  go,  which  constitute  the  wiggly  lines  shown  in  the 
photograph.  Most  of  the  ionization,  then,  which  is  pro- 
duced by  X-rays  is  a  secondary  effect  due  to  the  negative 
electrons,  i.e.,  the  /3-rays  which  the  X-rays  eject.  If 
these  /3-rays  could  in  turn  eject  electrons  with  ionizing 
speeds,  each  of  the  dots  in  one  of  these  /3-ray  tracks 
would  be  the  starting-point  of  a  new  wiggly  line  like  the 
original  one.  But  such  is  not  the  case.  We  may  think, 
then,  of  the  /3~rays  as  simply  shaking  loose  electronic 
dust  from  some  of  the  atoms  through  which  they  pass 
while  we  think  of  the  X-rays  as  taking  hold  in  some  way 
of  the  negative  electrons  within  an  atom  and  hurling 
them  out  with  enormous  energy. 


138  THE  ELECTRON 

V.      IONIZATION   BY   a-RAYS 

But  what  happens  to  the  electronic  constituents  of 
an  atom  when  an  a-particle,  that  is,  a  helium  atom, 
shoots  through  it?  Some  of  Bragg's  experiments  and 
Wilson's  photographs  show  that  the  a-particles  shoot 
in  straight  lines  through  from  3  to  7  cm.  of  air  before 
they  are  brought  to  rest.  We  must  conclude,  then,  that 
an  atom  has  so  loose  a  structure  that  another  atom,  if 
endowed  with  enough  speed,  can  shoot  straight  through  it 
without  doing  anything  more  than,  in  some  instances,  to 
shake  off  from  that  atom  an  electron  or  two.  The  tracks 
shown  in  Figs.  14  and  15,  p.  186,  are  Wilson's  photographs 
of  the  tracks  of  the  a-particles  of  radium.  They  ionize 
so  many  of  the  atoms  through  which  they  pass  that  the 
individual  droplets  of  water  which  form  about  the  ions 
produced  along  the  path  of  the  ray,  and  which  are  the 
objects  really  photographed,  are  not  distinguishable 
as  individuals.  The  sharp  changes  in  the  direction  of 
the  ray  toward  the  end  of  the  path  are  convincing 
evidence  that  the  a-particle  actually  goes  through 
the  atoms  instead  of  pushing  them  aside  as  does  a 
bullet.  For  if  one  solar  system,  for  example,  endowed 
with  a  stupendous  speed,  were  to  shoot  straight 
through  another  similar  system,  but  without  an  actual 
impact  of  their  central  bodies,  the  deflection  from  its 
straight  path  which  the  first  system  experienced  might 
be  negligibly  small  if  its  speed  were  high  enough,  and  that 
for  the  simple  reason  that  the  two  systems  would  not  be 
in  one  another's  vicinity  long  enough  to  produce  a 
deflecting  effect.  In  technical  terms  the  time  inte- 
gral of  the  force  would  be  negligibly  small.  The  slower 
the  speed,  however,  the  longer  this  time,  and  hence 


MECHANISM  OF  IONIZATION  OF  GASES        139 

the  greater  the  deflection.  Thus  it  is  only  when  the 
a-particle  shown  in  Fig.  15  has  lost  most  of  its  velocity — 
i.e.,  it  is  only  toward  the  end  of  its  path — that  the  nuclei 
of  the  atoms  through  which  it  passes,  are  able  to  deflect 
it  from  its  straight  path.  If  it  pushed  tne  molecules 
aside  as  a  bullet  does,  instead  of  going  through  them, 
the  resistance  to  its  motion  would  be  greatest  when  the 
speed  is  highest.  Now,  the  facts  are  just  the  opposite  of 
this.  The  a-particle  ionizes  several  times  more  violently 
toward  the  end  of  its  path  than  toward  the  beginning, 
and  it  therefore  loses  energy  more  rapidly  when  it  is  going 
slowly  than  when  it  is  going  rapidly.  Further,  it  is 
deflected  more  readily  then,  as  the  photograph  shows. 
All  of  this  is  just  as  it  should  be  if  the  a-particle  shoots 
straight  through  the  molecules  in  its  path  instead  of 
pushing  them  aside. 

These  photographs  of  Wilson's  are  then  the  most 
convincing  evidence  that  we  have  that  the  atom  is  a  sort 
of  miniature  stellar  system  with  constituents  which  are 
unquestionably  just  as  minute  with  respect  to  the  total 
volume  occupied  by  the  atom  as  are  the  sun  and  planets 
and  other  constituents  of  the  solar  system  with  respect 
to  the  whole  volume  inclosed  within  the  confines  of  this 
system.  When  two  molecules  of  a  gas  are  going  as 
slowly  as  they  are  in  the  ordinary  motion  of  thermal 
agitation,  say  a  mile  a  second,  when  their  centers  come 
to  within  a  certain  distance — about  o.  2  JJL/JL  (million  ths  of 
a  millimeter) — they  repel  one  another  and  so  the  two 
systems  do  not  inter-penetrate.  This  is  the  case  of  an 
ordinary  molecular  collision.  But  endow  one  of  these 
molecules  with  a  large  enough  energy  and  it  will  shoot 
right  through  the  other,  sometimes  doubtless  without  so 


140  THE  ELECTRON       . 

much  as  knocking  out  a  single  electron.  This  is  the  case 
of  an  a-particle  shooting  through  air. 

But  the  question  to  which  we  are  here  seeking  an 
answer  is,  does  the  a-particle  ever  knock  more  than  one 
electron  from  a  single  atom  or  molecule  through  which 
it  passes,  so  as  to  leave  that  atom  doubly  or  trebly 
charged?  The  oil-drop  method  used  at  low  pressures 
has  just  given  a  very  definite  negative  answer  to  this 
question.  In  no  gas  or  vapor  which  we  can  find,  and 
many,  including  mercury  compounds,  have  been  tried, 
does  an  a-ray  ever  knock  more  than  one  electron  from  a 
single  atom. 

J.  J.  Thomson  has,  however,  brought  forward  evi- 
dence1 that  the  positive  residues  of  atoms  which  shoot 
through  discharge  tubes  in  a  direction  opposite  to  that 
of  the  cathode  rays  do  sometimes  detach  several  electrons 
from  certain  kinds  of  atoms.  Indeed,  he  thinks  that  he 
has  evidence  that  the  ionization  of  a  mercury  atom  con- 
sists either  in  the  detachment  of  i  negative  electron  or 
else  in  the  detachment  of  8.  This  evidence,  too,  seems 
to  me  quite  convincing,  and  indeed  a  slow-moving 
positive  ray  may  well  do  more  damage  to  an  atom 
through  which  it  passes  than  a  high-speed  a-ray. 

VI.      SUMMARY 

The  results  of  the  studies  reviewed  in  this  chapter 
may  be  summarized  thus : 

i.  The  act  of  ionization  by  /3-rays  seems  to  consist 
in  the  shaking  off  without  any  appreciable  energy  of  one 
single  electron  from  an  occasional  molecule  through 

1  Rays  of  Positive  Electricity,  1913,  p.  46.  I 


MECHANISM  OF  IONIZATION  OF  GASES       ,141 

which  the  0-ray  passes.    The  faster  the  /3-ray  the  less 
frequently  does  it  ionize. 

2.  The  act  of  ionization  by  ether  waves,  i.e.,  by 
X-rays  or  light,  seems  to  consist  in  the  hurling  out  with 
an  energy  which  may  be  very  large,  but  which  depends 
upon  the  frequency  of  the  incident  ether  wave,  of  one 
single  electron  from  an  occasional  molecule  over  which 
this  wave  passes. 

3.  The  act  of  ionization  by  rapidly  moving  a-particles 
consists  in  the  shaking  loose  of  one  single  electron  from 
the  atom  through  which  it  passes1,  but  a  slow-moving 
positive  ray  appears  in  some  cases  to  be  able  to  detach 
several  electrons  from  a  single  atom. 

1  See  Gottschalk  and  Kelly,  Phys.  Rev.,  1917. 


CHAPTER  VII 

BROWNIAN  MOVEMENTS  IN  GASES 
I.      HISTORICAL   SUMMARY 

In  1827  the  English  botanist,  Robert  Brown,  first 
made  mention  of  the  fact  that  minute  particles  of  dead 
matter  in  suspension  in  liquids  can  be  seen  in  a  high- 
power  microscope  to  be  endowed  with  irregular  wiggling 
motions  which  strongly  suggest  "life."1  Although  this 
phenomenon  was  studied  by  numerous  observers  and 
became  known  as  the  phenomenon  of  the  Brownian 
movements,  it  remained  wholly  unexplained  for  just 
fifty  years.  The  first  man  to  suggest  that  these  motions 
were  due  to  the  continual  bombardment  to  which  these 
particles  are  subjected  because  of  the  motion  of  thermal 
agitation  of  the  molecules  of  the  surrounding  medium 
was  the  Belgian  Carbonelle,  whose  work  was  first  pub- 
lished by  his  collaborator,  Thirion,  in  i88o,2  although 
three  years  earlier  Delsaulx3  had  given  expression  to  views 
of  this  sort  but  had  credited  Carbonelle  with  priority  in 
adopting  them.  In  1881  Bodoszewski4  studied  the 
Brownian  movements  of  smoke  particles  and  other  sus- 
pensions in  air  and  saw  in  them  "an  approximate  image 
of  the  movements  of  the  gas  molecules  as  postulated  by 
the  kinetic  theory  of  gases."  Others,  notably  Gouy,5 

*Phtt.  Mag.,  IV  (1828),  161. 

3  Revue  des  questions  sdentifiques,  Louvain,  VII  (1880),  5. 
3  Ibid.,  II  (1877),  319. 

<  Dinglers  polyL  Jour.,  CCXXXIX  (1881),  325. 
s  Jour,  de  Phys.,  VII  (1888),  561;  Comptes  rendus,  CIX  (1889),  102. 
142 


BROWNIAN  MOVEMENTS  IN  GASES  143 

urged  during  the  next  twenty  years  the  same  interpre- 
tation, but  it  was  not  until  1905  that  a  way  was  found 
to  subject  the  hypothesis  to  a  quantitative  test.  Such 
a  test  became  possible  through  the  brilliant  theoretical 
work  of  Einstein1  of  Bern,  Switzerland,  who,  starting 
merely  with  the  assumption  that  the  mean  kinetic 
energy  of  agitation  of  a  particle  suspended  in  a  fluid 
medium  must  be  the  same  as  the  mean  kinetic  energy 
of  agitation  of  a  gas  molecule  at  the  same  temperature, 
developed  by  unimpeachable  analysis  an  expression  for 
the  mean  distance  through  which  such  a  particle  should 
drift  in  a  given  time  through  a  given  medium  because 
of  this  motion  of  agitation.  This  distance  could  be 
directly  observed  and  compared  with  the  theoretical 
value.  Thus,  suppose  one  of  the  wiggling  particles  is 
observed  in  a  microscope  and  its  position  noted  on  a 
scale  in  the  eyepiece  at  a  particular  instant,  then  noted 
again  at  the  end  of  r  (for  example,  10)  seconds,  and 
the  displacement  A#  in  that  time  along  one  particular 
axis  recorded.  Suppose  a  large  number  of  such  displace- 
ments A#  in  intervals  all  of  length  T  are  observed,  each  one 
of  them  squared,  and  the  mean  of  these  squares  taken 
and  denoted  by  A#*  :  Einstein  showed  that  the  theoretical 
value  of  Ar2  should  be 


in  which  R  is  the  universal  gas  constant  per  gram  mole- 
cule, namely,  83i.5Xios  deCg^es,  T  the  temperature  on 
the  absolute  scale,  N  the  number  of  molecules  in  one 
gram  molecule,  and  K  a  resistance  factor  depending 

•Ann.  d.  Phys.  (4),  XVII  (1905),  5495   XIX  (1906),  371;   XXII 
(1907),  569. 


144  THE  ELECTRON 

upon  the  viscosity  of  the  medium  and  the  size  of  the 
drop,  and  representing  the  ratio  between  the  force  ap- 
plied to  the  particle  in  any  way  and  the  velocity  pro- 
duced by  that  force.  If  Stokes's  Law,  namely,  F=6Trrjai^ 
held  for  the  motion  of  the  particle  through  the  medium, 

F 

then  K=—  would  have  the  value  67n?a,  so  that  Ein- 


v 
stein's  formula  would  become 


(22) 


This  was  the  form  which  Einstein  originally  gave  to 
his  equation,  a  very  simple  derivation  of  which  has  been 
given  by  Langevin.1  The  essential  elements  of  this 
derivation  will  be  found  in  Appendix  C. 

The  first  careful  test  of  this  equation  was  made  on 
suspensions  in  liquids  by  Perrin,2  who  used  it  for  finding 
N  the  number  of  molecules  in  a  gram  molecule.  He 
obtained  the  mean  value  ./V=68.  2Xio22,  which,  in  view 
of  the  uncertainties  in  the  measurement  of  both  K  and 
ir2,  may  be  considered  as  proving  the  correctness  of 
Einstein's  equation  within  the  limits  of  error  of  Perrin  's 
measurements,  which  differ  among  themselves  by  as 
much  as  30  per  cent. 

II.      QUANTITATIVE   MEASUREMENTS   IN   GASES 

Up  to  1909  there  had  been  no  quantitative  work 
whatever  on  Brownian  movements  in  gases.  Bodoszewski 
had  described  them  fully  and  interpreted  them  correctly 

1  Comptes  rendus,  CXLVI  (1908),  530. 

3  Ibid.,  p.  967;  CXLVII  (1908),  475,  530,  5945  CLII  (1911),  1380, 
1569;  see  also  Perrin,  Brownian  Movements  and  Molecular  Reality, 
Engl.  tr.  by  Soddy,  1912. 


BROWNIAN  MOVEMENTS  IN  GASES  145 

in  1 88 1.  In  1906  Smoluchowski1  had  computed  how 
large  the  mean  displacements  in  air  for  particles  of 
radius  a=  io~4  ought  to  be,  and  in  1907  Ehrenhaft2  had 
recorded  displacements  of  the  computed  order  with 
particles  the  sizes  of  which  he  made,  however,  no  attempt 
to  measure,  so  that  he  knew  nothing  at  all  about  the 
resistance  factor  K.  There  was  then  nothing  essentially 
quantitative  about  this  work. 

In  March,  1908,  De  Broglie,  in  Paris,3  made  the 
following  significant  advance.  He  drew  the  metallic 
dust  arising  from  the  condensation  of  the  vapors  coming 
from  an  electric  arc  or  spark  between  metal  electrodes 
(a  phenomenon  discovered  by  Hemsalech  and  De  Watte- 
ville4)  into  a  glass  box  and  looked  down  into  it  through 
a  microscope  upon  the  particles  rendered  visible  by  a 
beam  of  light  passing  horizontally  through  the  box  and 
illuminating  thus  the  Brownian  particles  in  the  focal 
plane  of  the  objective.  His  addition  consisted  in  placing 
two  parallel  metal  plates  in  vertical  planes,  one  on  either 
side  of  the  particles,  and  in  noting  that  upon  applying  a 
potential  difference  to  these  plates  some  of  the  particles 
moved  under  the  influence  of  the  field  toward  one  plate, 
some  remained  at  rest,  while  others  moved  toward  the 
other  plate,  thus  showing  that  a  part  of  these  particles 
were  positively  electrically  charged  and  a  part  negatively. 
In  this  paper  he  promised  a  study  of  the  charges  on  these 
particles.  In  May,  1909,  in  fulfilling  this  promise5  he 

1  Ann.  der  Phys.,  IV  (1906),  21,  756. 

2  Wiener  Berichte,  CXVI  (1907),  II,  1175. 

*  Comples  rendus,  CXLVI  (1908),  624,  1010. 
« Ibid.,  CXLIV  (1907),  1338. 
>Ibid.,  CXLVIII  (1909),  1316. 


146  THE  ELECTRON 

• 

made  the  first  quantitative  study  of  Brownian  move- 
ments in  gases.  The  particles  used  were  minute  droplets 
of  water  condensed  upon  tobacco  smoke.  The  average 
rate  at  which  these  droplets  moved  in  Broglie's  horizontal 
electric  field  was  determined.  The  equation  for  this 
motion  was 

Fe=Kv (23) 

The  mean  Ax2  was  next  measured  for  a  great  many 
particles  and  introduced  into  Einstein's  equation: 

—     2RT 

A  r2  — T 

~NKT' 

From  these  two  equations  K  was  eliminated  and  e 
obtained  in  terms  of  N.  Introducing  Perrin's  value  of 
N,  De  Broglie  obtained  from  one  series  of  measurements 
£=4.5Xio~10;  from  another  series  on  larger  particles 
he  got  a  mean  value  several  times  larger — -a  result  which 
he  interpreted  as  indicating  multiple  charges  on  the 
larger  particles.  Although  these  results  represent  merely 
mean  values  for  many  drops  which  are  not  necessarily  all 
alike,  either  in  radius  or  charge,  yet  they  may  be  con- 
sidered as  the  first  experimental  evidence  that  Einstein's 
equation  holds  approximately,  in  gases,  and  they  are  the 
more  significant  because  nothing  has  to  be  assumed  about 
the  size  of  the  particles,  if  they  are  all  alike  in  charge 
and  radius,  or  about  the  validity  of  Stokes's  Law  in 
gases,  the  ^-factor  being  eliminated. 

The  development  of  the  oil-drop  method  made  it 
possible  to  subject  the  Brownian-movement  theory  to  a 
more  accurate  and  convincing  experimental  test  than 
had  heretofore  been  attainable,  and  that  for  the  following 
reasons : 


BROWNIAN  MOVEMENTS  IN  GASES  147 

1.  It  made  it  possible  to  hold,  with  the  aid  of  the 
vertical   electrical   field,  one  particular  particle   under 
observation  for  hours  at  a  time  and  to  measure  as  many 
displacements  as  desired  on  it  alone  instead  of  assuming 
the  identity  of  a  great  number  of  particles,  as  had  been 
done  in  the  case  of  suspensions  in  liquids  and  in  De 
BroghVs  experiments  in  gases. 

2.  Liquids    are    very    much    less    suited    than   are 
gases   to   convincing   tests   of   any  kinetic  hypothesis, 
for    the    reason    that    prior    to    Brownian-movement 
work  we  had  no  satisfactory  kinetic  theory  of  liquids 
at  all. 

3.  The  absolute  amounts  of  the  displacements  of  a 
given  particle  in  air  are  8  times  greater  and  in  hydrogen 
15  times  greater  than  in  water. 

4.  By  reducing  the  pressure  to  low  values  the  dis- 
placements can  easily  be  made  from  50  to  200  times 
greater  in  gases  than  in  liquids. 

5.  The  measurements  can  be  made  independently 
of  the  most  troublesome  and  uncertain  factor  involved 
in  Brownian-movement  work  in  liquids,  namely,   the 
factor  K,  which  contains  the  radius  of  the  particle  and 
the  law  governing  its  motion  through  the  liquid. 

Accordingly,  there  was  begun  in  the  Ryerson  Lab- 
oratory, in  1910,  a  series  of  very  careful  experiments  in 
Brownian  movements  in  gases.  Svedberg,1  in  reviewing 
this  subject  in  1913,  considers  this  "the  only  exac.t 
investigation  of  quantitative  Brownian  movements  in 
gases."  A  brief  summary  of  the  method  and  results 
was  published  by  the  author.2  A  fyll  account  was 

1  Jahrbuch  der  Radioaktimtiit  und  Elektronik,  X  (1913),  513. 

2  Science,  February  17,  1911. 


148  THE  ELECTRON 

published  by  Mr.  Harvey  Fletcher  in  May,  191  1,1  and 
further  work  on  the  variation  of  Brownian  movements 
with  pressure  was  presented  by  the  author  the  year 
following.2  The  essential  contribution  of  this  work  as 
regards  method  consisted  in  the  two  following  particulars  : 
i.  By  combining  the  characteristic  and  fully  tested 
equation  of  the  oil-drop  method,  namely, 


(24) 


with  the  Einstein  Brownian-movement  equation,  namely, 
-r-      2RT 


it  was  possible  to  obtain  the  product  Ne  without  any 
reference  to  the  size  of  the  particle  or  the  resistance  of 
the  medium  to  its  motion.  This  quantity  could  then 
be  compared  with  the  same  product  obtained  with  great 
precision  from  electrolysis.  The  experimental  procedure 
consists  in  balancing  a  given  droplet  and  measuring,  as 
in  any  Brownian-movement  work,  the  quantity  Ax2,  then 
unbalancing  it  and  measuring  F,  vt  and  (^i+v2)0;  the 
combination  of  (24)  and  (25)  then  gives 


Ne 


Since  it  is  awkward  to  square  each  displacement  A# 
before  averaging,  it  is  preferable  to  modify  by  sub- 
stituting from  the  Maxwell  distribution  law,  which  holds 

*  Phys.  Zeitschr.,  XII  (1911),  202-8;    see  also  Phys.  Rev.,  XXXIII 
(IQTT),  81. 

a  Phys.  Rev.,  I,  N.S.  (1913),  218. 


BROWNIAN  MOVEMENTS  IN  GASES  149 

for  Brownian  displacements  as  well  as  for  molecular 
velocities,  the  relation 


We  obtain  thus 


or 


„ 
* 


The  possibility  of  thus  eliminating  the  size  of  the 
particle  and  with  it  the  resistance  of  the  medium  to  its 
motion  can  be  seen  at  once  from  the  simple  consideration 
that  so  long  as  we  are  dealing  with  one  and  the  same 
particle  the  ratio  K  between  the  force  acting  and  the 
velocity  produced  by  it  must  be  the  same,  whether  the 
acting  force  is  due  to  gravity  or  an  electrical  field,  as  in 
the  oil-drop  experiments,  or  to  molecular  impacts  as 
in  Brownian-movement  work.  De  Broglie  might  have 
made  such  an  elimination  and  calculation  of  Ne  in  his 
work,  had  his  Brownian  displacements  and  mobilities 
in  electric  fields  been  made  on  one  and  the  same  particle, 
but  when  the  two  sets  of  '  measurements  are  made  on 
different  particles,  such  elimination  would  involve  the 
very  uncertain  assumption  of  identity  of  the  particles  in 
both  charge  and  size.  Although  De  Broglie  did  actually 
make  this  assumption,  he  did  not  treat  his  data  in  the 
manner  indicated,  and  the  first  publication  of  this 
method  of  measuring  Ne  as  well  as  the  first  actual  deter- 
mination was  made  in  the  papers  mentioned  above. 


150  THE  ELECTRON 

Some  time  later  E.  Weiss  reported  similar  work  to 
the  Vienna  Academy.1 

2.  Although  it  is  possible  to  make  the  test  of  Ne  in 
just  the  method  described  and  although  it  was  so  made 
in  the  case  of  one  or  two  drops,  Mr.  Fletcher  worked  out 
a  more  convenient  method,  which  involves  expressing 
the  displacements  Ax  in  terms  of  the  fluctuations  in  the 
time  required  by  the  particle  to  fall  a  given  distance 
and  thus  dispenses  with  the  necessity  of  balancing  the 
drop  at  all.  I  shall  present  another  derivation  which 
is  very  simple  and  yet  of  unquestionable  validity. 

In  equation  (28)  let  T  be  the  time  required  by  the 
particle,  if  there  were  no  Brownian  movements,  to  fall 
between  a  series  of  equally  spaced  cross-hairs  whose 
distance  apart  is  d.  In  view  of  such  movements  the 
particle  will  have  moved  up  or  down  a  distance  Ax  in 
the  time  T.  Let  us  suppose  this  distance  to  be  up. 
Then  the  actual  time  of  fall  will  be  r+AJ,  in  which  At 
is  now  the  time  it  takes  the  particle  to  fall  the  distance 
Ax.  If  now  A/  is  small  in  comparison  with  r,  that  is,  if 
Ax  is  small  in  comparison  with  d  (say  i/io  or  less),  then 
we  shall  introduce  a  negligible  error  (of  the  order  i/ioo 
at  the  most)  if  we  assume  that  Ax  =  ViAt  in  which  ^  is 
the  mean  velocity  under  gravity.  Replacing  then  in 
(28)  (AxY  byvl2(AtY,  in  which  (KtY  is  the  square  of  the 
average  difference  between  an  observed  time  of  fall  and 
the  mean  time  of  fall  tg,  that  is,  the  square  of  the  average 

1  It  was  read  before  the  Academy  on  July  6 :  Wiener  Berichte,  CXX 
(1911),  II,  1021,  but  appeared  first  in  print  in  the  August  ist  number 
of  the  Phys.  Zeitschr.  (1911),  p.  63.  Fletcher's  article  is  found  in  brief 
in  an  earlier  number  of  the  same  volume  of  the  Phys.  Zeitschr.,  p.  203, 
and  was  printed  in  full  in  the  July,  number  of  Le  Radium,  VIII 
(1911),  279. 


BROWNIAN  MOVEMENTS  IN  GASES  151 

fluctuation  in  the  time  of  fall  through  the  distance  d, 
we  obtain  after  replacing  the  ideal  time  T  by  the  mean 
time  t\ 

tRTdt+vJJ, 

-~~  ..............  (29) 


In  any  actual  work  A/  will  be  kept  considerably  less 
than  i/io  the  mean  time  tg  if  the  irregularities  due  to 
the  observer's  errors  are  not  to  mask  the  irregularities 
due  to  the  Brownian  movements,  so  that  (29)  is  sufficient 
for  practically  all  working  conditions.1 

The  work  of  Mr.  Fletcher  and  of  the  author  was  done 
by  both  of  the  methods  represented  in  equations  (28) 
and  (29).  The  9  drops  reported  upon  in  Mr.  Fletcher's 
paper  in  i9ii2  yielded  the  results  shown  below  in  which 
n  is  the  number  of  displacements  used  in  each  case  in 
determining  Ax  or  A/.  • 

TABLE  XIII 


1.68  125 
1  .  67  136 
1.645  321 

.  695  2O2 

•  73         171 

.65  20O 

.66         84 

.785      411 

•65         85 

When  weights  are  assigned  proportional  to  the  num- 
ber of  observations  taken,  as  shown  in  the  last  column 

1  No  error  is  introduced  here  if,  as  assumed,  A/  is  small  in  comparison 
with  tg.  However,  for  more  rigorous  equations  see  Fletcher,  Phys.  Rev., 
IV  (1914),  442;  also  Smoluchowski,  Phys.  Zeitschr.,  XVI  (1915),  321. 

1  Le  Radium,  VIII  (1911),  279;  Phys.  Rev.,  XXXIII  (1911),  107. 


152  THE  ELECTRON 

of  Table  XIII,  there  results  for  the  weighted  mean  value 
which  represents  an  average  of  1,735  displacements, 
l/A^=i.698Xio7  or  Ne=2.SSXio14  electrostatic  units, 
as  against  2.896Xio14,  the  value  found  in  electroly- 
sis. The  agreement  between  theory  and  experiment  is 
then  in  this  case  about  as  good  as  one-half  of  i  per  cent, 
which  is  well  within  the  limits  of  observational  error. 

This  work  seemed  to  demonstrate,  with  considerably 
greater  precision  than  had  'been  attained  in  earlier 
Brownian-movement  work  and  with  a  minimum  of 
assumptions,  the  correctness  of  the  Einstein  equation, 
which  is  in  essence  merely  the  assumption  that  a  particle 
in  a  gas,  no  matter  how  big  or  how  little  it  is  or  out  of 
what  it  is  made,  is  moving  about  with  a  mean  translatory 
kinetic  energy  which  is  a  universal  constant  dependent 
only  on  temperature.  To  show  how  well  this  conclusion 
has  been  established  I  shall  refer  briefly  to  a  few  later 
researches. 

In  1914  Dr.  Fletcher,  assuming  the  value  of  K  which 
I  had  published1  for  oil  drops  moving  through  air,  made 
new  and  improved  Brownian-movement  measurements 
in  this  medium  and  solved  for  N  the  original  Einstein 
equation,  which,  when  modified  precisely  as  above  by 

replacing  A#2  by  —  (AJ)    and  (5#)  =Vj.2(At)    becomes 


(30) 


He  took,  all  told,  as  many  as  18,837  A/'s,  n°t  ^ess  than 
5,  900  on  a  single  drop,  and  obtained  ./V=6o.  3X10"  =*=  1.2. 
This  cannot  be  regarded  as  an  altogether  indepen- 
dent determination  of  N,  since  it  involves  my  value 

1  Phys.  Rev.,  I  (1913),  218. 


BROWNIAN  MOVEMENTS  IN  GASES  153 

of  K.  Agreeing,  however,  as  well  as  it  does  with  my 
value  of  N ',  it  does  show  with  much  conclusiveness  that 
both  Einstein's  equation  and  my  corrected  form  of 
Stokes's  equation  apply  accurately  to  the  motion  of  oil 
drops  of  the  size  here  used,  namely,  those  of  radius  from 
2.79Xio~scm.  to  4.iXio~scm.  (280—400  /z^u). 

In  1915  Mr.  Carl  Eyring  tested  by  equation  (29)  the 
value  of  Ne  on  oil  drops,  of  about  the  same  size,  in 
hydrogen  and  came  out  within  .  6  per  cent  of  the  value 
found  in  electrolysis,  the  probable  error  being,  however, 
some  2  per  cent. 

Precisely  similar  tests  on  substances  other  than  oils 
were  made  by  Dr.  E.  Weiss1  and  Dr.  Karl  Przibram.2 
The  former  worked  with  silver  particles  only  half 
as  large  as  the  oil  particles  mentioned  above,  namely, 
of  radii  between  i  and  2.3Xio~5  cm.  and  obtained 
Ne=  10,700  electromagnetic  units  instead  of  9,650.  as 
in  electrolysis.  This  is  indeed  n  per  cent  too  high,  but 
the  limits  of  error  in  Weiss's  experiments  were  in  his 
judgment  quite  as  large  as  this.  K.  Przibram  worked 
on  suspensions  in  air  of  five  or  six  different  substances, 
the  radii  varying  from  200  ju/z  to  600  juju,  and  though  his 
results  varied  among  themselves  by  as  much  as  100  per 
cent,  his  mean  value  came  within  6  per  cent  of  9,650. 
Both  of  the  last  two  observers  took  too  few  displacements 
on  a  given  drop  to  obtain  a  reliable  mean  displacement, 
but  they  used  so  many  drops  that  their  mean  Ne  still 
has  some  significance. 

It  would  seem,  therefore,  that  the  validity  of  Ein- 
stein's Brownian-movement  equation  had  been  pretty 

'  Sitzungsber.  d.  k.  Akad.  d.  Wiss.  in  Wien,  CXX  (1911),  II,  1021. 
1  Ibid.,  CXXI  (1912),  II,  950. 


154  THE  ELECTRON 

thoroughly  established  in  gases.  In  liquids  too  it  has 
recently  been  subjected  to  much  more  precise  test  than 
had  formerly  been  attained.  Nordlund,3  in  1914,  using 
minute  mercury  particles  in  water  and  assuming  Stokes's 
Law  of  fall  and  Einstein's  equations,  obtained 
N=S9-  iXio21.  While  in  1915  Westgren  at  Stockholm4 
by  a  very  large  number  of  measurements  on  colloidal 
gold,  silver,  and  selenium  particles,  of  diameter  from 
65  HIJL  to  130  up  (6.5  to  13 X  io~6  cm.),  obtained  a  result 
which  he  thinks  is  correct  to  one-half  of  i  per  cent,  this 
value  is  N  =  60 . 5  X  i  o22  =*= .  3  X  i o22 ,  which  agrees  per- 
fectly with  the  value  which  I  obtained  from  the  measure- 
ments on  the  isolation  and  measurement  of  the  electron. 
It  has  been  because  of  such  agreements  as  the  fore- 
going that  the  last  trace  of  opposition  to  the  kinetic  and 
atomic  hypotheses  of  matter  has  disappeared  from  the 
scientific  world,  and  that  even  Ostwald  has  been  willing 
to  make  such  a  statement  as  that  quoted  on  p.  10  above. 

3  Ztschr.f.  Phys.  Ckem.,  LXXXVII  (1914),  40. 

4  Die  Brown'sche  Bewegung  besonders  als  Mittel  zur  Bestimmung  der 
Avogadroschen  Konstante,  inaugural  dissertation.    Upsala:    Almquist  & 
Wiksells  Boktryckeri,  1915. 


CHAPTER  VIII 
THE  EXISTENCE  OF  A  SUB-ELECTRON? 

It  would  not  be  in  keeping  with  the  ntethod  of  modern 
science  to  make  any  dogmatic  assertion  as  to  the  indi- 
visibility of  the  electron.  Such  assertions  used  to  be 
made  in  high-school  classes  with  respect  to  the  atoms  of 
the  elements,  but  the  far-seeing  among  physicists,  like 
Faraday,  were  always  careful  to  disclaim  any  belief  in 
the  necessary  ultimateness  of  the  atoms  of  chemistry,  and 
that  simply  because  there  existed  until  recently  no  basis 
for  asserting  anything  about  the  insides  of  the  atom. 
We  knew  that  there  was  a  smallest  thing  which  took  part 
in  chemical  reactions  and  we  named  that  thing  the  atom, 
leaving  its  insides  entirely  to  the  future. 

Precisely  similarly  the  electron  was  denned  as  the 
smallest  quantity  of  electricity  which  ever  was  found  to 
appear  in  electrolysis,  and  nothing  was  then  said  or  is 
now  said  about  its  necessary  ultimateness.  Our  experi- 
ments have,  however,  now  shown  that  this  quantity  is 
capable  of  isolation  and  exact  measurement,  and  that  all 
the  kinds  of  charges  which  we  have  been  able  to  investi- 
gate are  exact  multiples  of  it.  Its  value  is  4. 774X  io~10 
electrostatic  units. 

I.      A   SECOND  METHOD   OF   OBTAINING  e 

I  have  presented  one  way  of  measuring  this  charge, 
but  there  is  an  indirect  method  of  arriving  at  it  which 
was  worked  out  independently  by  Rutherford  and  Geiger1 

1  Proc.  Roy.  Soc.,  A  LXXXI  (1908),  141,  161. 
155 


156  THE  ELECTRON 

and  Regener.1  The  unique  feature  in  this  method  con- 
sists in  actually  counting  the  number  of  a-particles  shot 
off  per  second  by  a  small  speck  of  radium  or  polonium 
through  a  given  solid  angle  and  computing  from  this  the 
number  of  these  particles  emitted  per  second  by  one  gram 
of  the  radium  or  polonium.  Regener  made  his  determi- 
nation by  counting  the  scintillations  produced  on  a  dia- 
mond screen  in  the  focal  plane  of  his  observing  microscope. 
He  then  caught  in  a  condenser  all  the  a-particles  emitted 
per  second  by  a  known  quantity  of  his  polonium  and 
determined  the  total  quantity  of  electricity  delivered  to 
the  condenser  by  them.  This  quantity  of  electricity 
divided  by  the  number  of  particles  emitted  per  second 
gave  the  charge  on  each  particle.  Because  the  a-particles 
had  been  definitely  proved  to  be  helium  atoms2  and  the 

value  of  --  found  for  them  showed  that  if  they  were 
m 

helium  they  ought  to  carry  double  the  electronic  charge, 
Regener  divided  his  result  by  2  and  obtained 


He  estimated  his  error  at  3  per  cent.  Rutherford  and 
Geiger  made  their  count  by  letting  the  a-particles  from 
a  speck  of  radium  C  shoot  into  a  chamber  and  produce 
therein  sufficient  ionization  by  collision  to  cause  an 
electrometer  needle  to  jump  every  time  one  of  them 
entered.  These  authors  measured  the  total  charge  as 
Regener  did  and,  dividing  by  2  the  charge  on  each 
a-particle,  they  obtained 

£=4.65X10-'°. 

*Sitzungsber.  d.  k.  Preuss.  Akad.,  XXXVIII  (1909),  948. 
2  Rutherford  and  Royds,  Phil.  Mag.,  XVII  (1909),  281. 


THE  EXISTENCE  OF  A  SUB-ELECTRON  ?        157 

All  determinations  of  e  from  radioactive  data  involve 
one  or  the  other  of  these  two  counts,  namely,  that  of 
Rutherford  and  Geiger  or  that  of  Regener.  Thus, 
Boltwood  and  Rutherford1  measured  the  total  weight  of 
helium  produced  in  a  second  by  a  known  weight  of 
radium.  Dividing  this  by  the  number  of  a-particles 
(helium  atoms)  obtained  from  Rutherford  and  Geiger's 
count,  they  obtain  the  mass  of  one  atom  of  helium  from 
which  the  number  in  a  given  weight,  or  volume  since  the 
gas  density  is  known,  is  at  once  obtained.  They  pub- 
lished for  the  number  n  of  molecules  in  a  gas  per  cubic 
centimeter  at  o?76  cm.,  w=2.6gXio19,  which  corre- 
sponds to 


This  last  method,  like  that  of  the  Brownian  movement, 
is  actually  a  determination  of  N,  rather  than  of  e,  since 
e  is  obtained  from  it  only  through  the  relation  ^=9,650 
electromagnetic  units.  Indeed,  this  is  true  of  all 
methods  of  estimating  e,  so  far  as  I  am  aware,  except  the 
oil-drop  method  and  the  Rutherford-Geiger-Regener 
method,  and  of  these  two  the  latter  represents  the 
measurement  of  the  mean  charge  on  an  immense  number 
of  a-particles. 

Thus  a  person  who  wished  to  contend  that  the  unit 
charge  appearing  in  electrolysis  is  only  a  mean  charge 
which  may  be  made  up  of  individual  charges  which  vary 
widely  among  themselves,  in  much  the  same  way  in 
which  the  atomic  weight  assigned  to  neon  has  recently 
been  shown  to  be  a  mean  of  the  weights  of  at  least  two 
different  elements  inseparable  chemically,  could  not  be 
gainsaid,  save  on  the  basis  of  the  evidence  contained  in 

1  Phil  Mag.  (6),  XXII  (IQII),  599. 


158  THE  ELECTRON 

the  oil-drop  experiments;  for  these  constitute  the  only 
method  which  has  been  found  of  measuring  directly  the 
charge  on  each  individual  ion.  It  is  of  interest  and  sig- 
nificance for  the  present  discussion,  however,  that  the 
mean  charge  on  an  a-particle  has  been  directly  measured 
and  that  it  comes  out,  within  the  limits  of  error  of  the 
measurement,  at  exactly'  two  electrons — -as  it  should 

s> 

according  to  the  evidence  furnished  by  —  measurements 
on  the  a-particles. 

II.      THE  EVIDENCE  FOR  THE  EXISTENCE  OF  A  SUB- 
ELECTRON 

Now,  the  foregoing  contention  has  actually  been  made 
recently,  and  evidence  has  been  presented  which  purports 
to  show  that  electric  charges  exist  which  are  much 
smaller  than  the  electron.  Since  this  raises  what  may 
properly  be  called  the  most  fundamental  question  of 
modern  physics,  the  evidence  needs  very  careful  con- 
sideration. This  evidence  can  best  be  appreciated 
through  a  brief  historical  review  of  its  origin. 

The  first  measurements  on  the  mobilities  in  electric 
fields  of  swarms  of  charged  particles  of  microscopically 
visible  sizes  were  made  by  H.  A.  Wilson1  in  1903,  as 
detailed  in  chap.  iii.  These  measurements  were  repeated 
with  modifications  by  other  observers,  including  our 
selves,  during  the  years  immediately  following.  De 
Broglie's  modification,  published  in  1908,*  consisted  in 
sucking  the  metallic  clouds  discovered  by  Hemsalech 
and  De  Watteville,3  produced  by  sparks  or  arcs  between 

-Phil.  Mag.  (6),  V  (1903),  429- 

2  Com  pies  rendus,  CXLVI  (1908),  624,  1010. 

3/Wtf.,  CXLIV  (1907),  1338. 


THE  EXISTENCE  OF  A  SUB-ELECTRON?        159 

metal  electrodes,  into  the  focal  plane  of  an  ultra- 
microscope  and  observing  the  motions  of  the  individual 
particles  in  this  cloud  in  a  horizontal  electrical  field  pro- 
duced by  applying  a  potential  difference  to  two  vertical 
parallel  plates  in  front  of  the  objective  of  his  microscope. 
In  this  paper  De  Broglie  first  commented  upon  the  fact 
that  some  of  these  particles  were  charged  positively, 
some  negatively,  and  some  not  at  all,  and  upon  the 
further  fact  that  holding  radium  near  the  chamber 
caused  changes  in  the  charges  of  the  particles.  He 
promised  quantitative  measurements  of  the  charges 
themselves.  One  year  later  he  fulfilled  the  promise,1 
and  at  practically  the  same  time  Ehrenhaft2  published 
similar  measurements  made  with  precisely  the  arrange- 
ment described  by  De  Broglie  a  year  before.  Both  men, 
as  Ehrenhaft  clearly  pointed  out,3  while  observing  indi- 
vidual particles,  obtained  only  a  mean  charge,  since  the 
different  measurements  entering  into  the  evaluation  of  e 
were  made  on  different  particles.  So  far  as  concerns  e, 
these  measurements,  as  everyone  agrees,  were  essentially 
cloud  measurements  like  Wilson's. 

In  the  spring  and  summer  of  1909  I  isolated  indi- 
vidual water  droplets  and  determined  the  charges  car- 
ried by  each  one,4  and  in  April,  1910,  I  read  before  the 
American  Physical  Society  the  full  report  on  the  oil-drop 
work  in  which  the  multiple  relations  between  charges  were 
established,  Stokes's  Law  corrected,  and  e  accurately 

*Ibid.t  CXLVIII  (1909),  1316. 
3  Phys.  Zeitschr.,  X  (1909),  308. 

3  Ibid.,  XI  (1910),  619. 

4  This  paper  was  published  in  abstract  in  Phys.  Rev.,  XXX  (1909), 
560,  and  Phil.  Mag.,  XIX  (1910),  209. 


:6o  THE  ELECTRON 

determined.1  In  the  following  month  (May,  1910) 
Ehrenhaft,2  having  seen  that  a  vertical  condenser 
arrangement  made  possible,  as  shown  theoretically  and 
experimentally  in  the  1909  papers  mentioned  above,  the 
independent  determination  of  the  charge  on  each  indi- 
vidual particle,  read  the  first  paper  in  which  he  had  used 
this  arrangement  in  place  of  the  De  Broglie  arrange- 
ment which  he  had  used  theretofore.  He  reported  re- 
sults identical  in  all  essential  particulars  with  those 
which  I  had  published  on  water  drops  the  year  before, 
save  that  where  I  obtained  consistent  and  simple  multiple 
relations  between  charges  carried  by  different  particles 
he  found  no  such  consistency  in  these  relations.  The 
absolute  values  of  these  charges  obtained  on  the  as- 
sumption of  Stokes's  Law  fluctuated  about  values  con- 
siderably lower  than  4.6Xio~10.  Instead,  however,  of 
throwing  the  burden  upon  Stokes's  Law  or  upon  wrong 
assumptions  as  to  the  density  of  his  particles,  he  re- 
marked in  a  footnote  that  Cunningham's  theoretical  cor- 
rection to  Stokes's  Law,3  which  he  (Ehrenhaft)  had  just 
seen,  would  make  his  values  come  still  lower,  and  hence 
that  no  failure  of  Stokes's  Law  could  be  responsible 
for  his  low  values.  He  considered  his  results  therefore 
as  opposed  to  the  atomic  theory  of  electricity  altogether, 
and  in  any  case  as  proving  the  existence  of  charges  much 
smaller  than  that  of  the  electron.4 

1  This  paper  was  published  in  abstract  in  Phys.  Rev.,  XXXI  (1910), 
92;   Science,  XXXII  (1910),  436;  Phys.  Zeilschr.,  XI  (1910),  1097. 

2  Wien.  Ber.,  CXIX  (1910),  II,  809.    This  publication  was  appar- 
ently not  issued  before  December,  1910,  for  it  is  not  noted  in  Naturae 
Novitales  before  this  date. 

3  Proc.  Roy.  Soc.,  LXXXIII  (1910),  360. 

"  These  results  were  presented  and  discussed  at  great  length  in  the 
fall  of  1910;   see  Phys.  Zeilschr.,  XI  (1910),  619,  940. 


THE  EXISTENCE  OF  A  SUB-ELECTRON?        161 

The  apparent  contradiction  between  these  results  and 
mine  was  explained  when  Mr.  Fletcher  and  myself 
showed1  experimentally  that  Brownian  movements  pro- 
duced just  such  apparent  fluctuations  as  Ehrenhaft 
observed  when  the  e  is  computed,  as  had  been  done  in 
his  work,  from  one  single  observation  of  a  speed  under 
gravity  and  a  corresponding  one  in  an  electric  field.  We 
further  showed  that  the  fact  that  his  values  fluctuated 
about  too  low  an  average  value  meant  simply  that  his 
particles  of  gold,  silver,  and  mercury  were  less  dense 
because  of  surface  impurities,  oxides  or  the  like,  than  he 
had  assumed.  The  correctness  of  this  explanation 
would  be  well-nigh  demonstrated  if  the  values  of  Ne 
computed  by  equations  (28)  or  (29)  in  chap,  vii  from  a 
large  number  of  observations  on  Brownian  movements 
always  came  out  as  in  electrolysis,  for  in  these  equations 
no  assumption  has  to  be  made  as  to  the  density  of  the 
particles.  As  a  matter  of  fact,  all  of  the  nine  particles 
studied  by  us  and  computed  by  Mr.  Fletcher2  showed 
the  correct  value  of  Ne,  while  only  six  of  them  as  com- 
puted by  me  fell  on,  or  close  to,  the  line  which  pictures 
the  law  of  fall  of  an  oil  drop  through  air  (Fig.  5,  p.  104). 
This  last  fact  was  not  published  in  1911  because  it  took 
me  until  1913  to  determine  with  certainty  the  complete 
law  of  fall  of  a  droplet  through  air;  in  other  words,  to 
extend  curves  of  the  sort  given  in  Fig.  5  to  as  large 

values  of  -  as  correspond  to  particles  small  enough  to 

show  large  Brownian  movements.     As  soon  as  I  had 
done  this  I  computed  all  the  nine  drops  which  gave  cor- 

1  Phys.  Zeitschr.,  XII  (1911),  161;  Phys.  Rev.,  XXXII  (1911),  394- 
2Le  Radium,  VIII  (1911),  279;  Phys.  Rev.,  XXXIII  (1911),  107. 


162  THE  ELECTRON 

rect  values  of  Ne  and  found  that  two  of  them  fell  way 
below  the  line,  one  more  fell  somewhat  below,  while  one 
fell  considerably  above  it.  This  meant  obviously  that 
these  four  particles  were  not  spheres  of  oil  alone,  two  of 
them  falling  much  too  slowly  to  be  so  constituted  and 
one  considerably  too  rapidly.  There  was  nothing  at  all 
surprising  about  this  result,  since  I  had  explained  fully 
in  my  first  paper  on  oil  drops1  that  until  I  had  taken 
great  precaution  to  obtain  dust-free  air  "the  values  of  el 
came  out  differently,  even  for  drops  showing  the  same 
velocity  under  gravity."  In  the  Brownian-movement 
work  no  such  precautions  to  obtain  dust-free  air  had 
been  taken  because  we  wished  to  test  the  general  validity 
of  equations  (28)  and  (29) .  That  we  actually  used  in  this 
test  two  particles  which  had  a  mean  density  very  much 
smaller  than  that  of  oil  and  one  which  was  considerably 
too  heavy,  was  fortunate  since  it  indicated  that  our 
result  was  indeed  independent  of  the  material  used. 

It  is  worthy  of  remark  that  in  general,  even  with  oil 
drops,  almost  all  of  those  behaving  abnormally  fall  too 
slowly,  that  is,  they  fall  below  the  line  of  Fig.  5  and 
only  rarely  does  one  fall  above  it.  This  is  because  the 
dust  particles  which  one  is  likely  to  observe,  that  is,  those 
which  remain  long  in  suspension  in  the  air,  are  either  in 
general  lighter  than  oil  or  else  expose  more  surface  and 
hence  act  as  though  they  were  lighter.  When  one  works 
with  particles  made  of  dense  metals  this  behavior  will 
be  still  more  marked,  since  all  surface  impurities  of  what- 
ever sort  will  diminish  the  density.  The  possibility, 
however,  of  freeing  oil-drop  experiments  from  all  such 
sources  of  error  is  shown  by  the  fact  that  although  during 

'  Phys.  Rev.,  XXXIII  (1911),  366,  367. 


THE  EXISTENCE  OF  A  SUB-ELECTRON?        163 

the  past  year  I  have  studied  altogether  as  many  as  three 
hundred  drops,  there  has  not  been  a  single  case  that  I 
can  recall  which  did  not  fall  within  less  than  i  per  cent 
of  the  line  of  Fig.  5.  It  will  be  shown,  too,  in  this 
chapter,  that  in  spite  of  the  failure  of  the  Vienna  experi- 
menters, it  is  possible  to  obtain  mercury  drops  which 
behave,  even  as  to  law  of  fall,  in  practically  all  cases  with 
perfect  consistency  and  normality. 

When  E.  Weiss  in  Prag  and  K.  Przibram  in  the 
Vienna  laboratory  itself,  as  explained  in  chap,  vii,  had 
found  that  Ne  for  all  the  substances  which  they  worked 
with,  including  silver  particles  like  those  used  by 
Ehrenhaft,  gave  about  the  right  value  of  .Ne,  although 
yielding  much  too  low  values  of  e  when  the  latter  was 
computed  from  the  law  of  fall  of  silver  particles,  the 
scientific  world  practically  universally  accepted  our 
explanation  of  Ehrenhaft's  results  and  ceased  to  concern 
itself  with  the  idea  of  a  sub-electron.1 

In  1914  and  1915,  however,  Professor  Ehrenhaft2  and 
two  of  his  pupils,  F.  Zerner3  and  D.  Konstantinowsky,4 
published  new  evidence  for  the  existence  of  such  a  sub- 
electron.  This  evidence  appears  to  be  but  little  under- 
stood and  therefore  calls  for  some  comment.  These 
authors  make  three  contentions.  The  first  is  essentially 
that  they  have  now  determined  Ne  for  their  particles  by 
equation  (29) ;  and  although  in  many  instances  it  comes 
.out  as  in  electrolysis,  in  some  instances  it  comes  out  from 

1  See  R.  Pohl,  Jahrbuch  der  Radioactimtat  und  Elektronik,  VIII 
(1912),  431. 

8  Wien.  Sitzungsber.,  CXXIII  (1914),  53-155;  Ann.  d.  Pkys.,  XLIV 
(1914),  657. 

a  Phys.  Zeitschr.,  XVI  (1915),  10. 

*  Ann.  d.  Phys.,  XL VI  (1915),  261. 


164  THE  ELECTRON 

20  per  cent  to  50  per  cent  too  low,  while  in  a  few  cases 
it  is  as  low  as  one-fourth  or  one-fifth  of  the  electrolytic 
value.  Their  procedure  is  in  general  to  publish,  not  the 
value  of  Ne,  but,  instead,  the  value  of  e  obtained  from 
Ne  by  inserting  Perrin's  value  of  N  (joX  io22)  in  (29)  and 
then  solving  for  e.  This  is  their  method  of  determining 
e  "from  the  Brownian  movements.'7 

Their  second  contention  is  the  same  as  that  originally 
advanced,  namely,  that,  in  some  instances,  when  e  is 
determined  with  the  aid  of  Stokes 's  Law  of  fall  (equa- 
tion 12,  p.  89),  even  when  Cunningham's  correction  or 
my  own  (equation  15,  p.  99)  is  employed,  the  result 
comes  out  very  much  lower  than  4.77Xio~10.  Their 
third  claim  is  that  the  value  of  e,  determined  as  just 
explained  from  the  Brownian  movements,  is  in  general 
higher  than  the  value  computed  from  the  law  of  fall, 
and  that  the  departures  become  greater  and  greater  the 
smaller  the  particle.  These  observers  conclude  therefore 
that  we  at  the  Ryerson  Laboratory  failed  to  detect  sub- 
electrons  because  our  droplets  were  too  big  to  be  able  to 
reveal  their  existence.  The  minuter  particles  which  they 
study,  however,  seem  to  them  to  bring  these  sub- 
electrons  to  light.  In  other  words,  they  think  the  value 
of  the  smallest  charge  which  can  be  caught  from  the  air 
actually  is  a  function  of  the  radius  of  the  drop  on  which 
it  is  caught,  being  smaller  for  small  drops  than  for  large 
ones. 

Ehrenhaft  and  Zerner  even  analyze  our  reports  on  oil 
droplets  and  find  that  these  also  show  in  certain  instances 
indications  of  sub-electrons,  for  they  yield  in  these 
observers'  hands  too  low  values  of  e,  whether  computed 
from  the  Brownian  movements  or  from  the  law  of  fall. 


THE  EXISTENCE  OF  A  SUB-ELECTRON  ?        165 

When  the  computations  are  made  in  the  latter  way  e  is 
found,  according  to  them,  to  decrease  with  decreasing 
radius,  as  is  the  case  in  their  experiments  on  particles  of 
mercury  and  gold. 

III.      CAUSES   OF  THE  DISCREPANCIES 

Now,  the  single  low  value  of  Ne  which  these  authors 
find  in  the  oil-drop  work  is  obtained  by  computing  Ne 
from  some  twenty-five  observations  on  the  times  of  fall, 
and  an  equal  number  on  the  times  of  rise,  of  a  particle 
which,  before  we  had  made  any  Ne  computations  at  all, 
we  reported  upon1  for  the  sake  of  showing  that  the 
Brownian  movements  would  produce  just  such  fluctua- 
tions as  Ehrenhaft  had  observed  when  the  conditions 
were  those  under  which  he  worked.  When  I  compute 
Ne  by  equation  (29),  using  merely  the  twenty-five  times 
of  fall,  I  find  the  value  of  Ne  comes  out  26  per  cent  low, 
just  as  Zerner  finds  it  to  do.  If,  however,  I  omit  the 
first  reading  it  comes  out  but  1 1  per  cent  low.  In  other 
words,  the  omission  of  one  single  reading  changes  the 
result  by  15  per  cent.  Furthermore,  Fletcher2  has  just 
shown  that  these  same  data,  though  treated  entirely 
legitimately,  but  with  a  slightly  different  grouping  than 
that  used  by  Zerner,  can  be  made  to  yield  exactly  the 
right  value  of  Ne.  This  brings  out  clearly  the  futility 
of  attempting  to  test  a  statistical  theorem  by  so  few 
observations  as  twenty-five,  which  is  nevertheless  more 
than  Ehrenhaft  usually  uses  on  his  drops.  Furthermore, 
I  shall  presently  show  that  unless  one  observes  under 
carefully  chosen  conditions,  his  own  errors  of  observation 

1  Phys.  Zeitschr.,  XII  (1911),  162. 

2  Ibid.,  XVI  (1915),  316. 


1 66  THE  ELECTRON 

and  the  slow  evaporation  of  the  drop  tend  to  make  Ne 
obtained  from  equation  (29)  come  out  too  low,  and  these 
errors  may  easily  be  enough  to  vitiate  the  result  entirely. 
There  is,  then,  not  the  slightest  indication  in  any  work 
which  we  have  thus  far  done  on  oil  drops  that  Ne  comes 
out  too  small. 

Next  consider  the  apparent  variation  in  e  when  it  is 
computed  from  the  law  of  fall.  Zerner  computes  e  from 
my  law  of  fall  in  the  case  of  the  nine  drops  published  by 
Fletcher,  in  which  Ne  came  out  as  in  electrolysis,  and 
finds  that  one  of  them  yields  e  =  6.66Xio"~10,  one 
tf=3.97Xio~10,  one  e=i.32Xio~10,  one  e=i.'jXio~10, 
while  the  other  five  yield  about  the  right  value,  namely, 
4. 8X  io~10.  In  other  words  (as  stated  on  p.  162  above), 
five  of  these  drops  fall  exactly  on  my  curve  (Fig.  5),  one 
falls  somewhat  above  it,  one  somewhat  below,  while  two 
are  entirely  off  and  very  much  too  low.  These  two,  there- 
fore, I  concluded  were  not  oil  at  all,  but  dust  particles. 
Since  Zerner  computes  the  radius  from  the  rate  of  fall, 
these  two  dust  particles  which  fall  much  too  slowly,  and 
therefore  yield  too  low  values  of  e,  must,  of  course,  yield 
correspondingly  low  values  of  a.  Since  they  are  found 
to  do  so,  Zerner  concludes  that  our  oil  drops,  as  well  as 
Ehrenhaft's  mercury  particles,  yield  decreasing  values  of 
e  with  decreasing  radius.  His  own  tabulation  does  not 
show  this.  It  merely  shows  three  erratic  values  of  e, 
two  of  which  are  very  low  and  one  rather  high.  But  a 
glance  at  all  the  other  data  which  I  have  published  on 
oil  drops  shows  the  complete  falsity  of  this  position,1  for 
these  data  show  that  after  I  had  eliminated  dust  all  of  my 
particles  yielded  exactly  the  same  value  oflie"  whatever  their 

'  Phys.  Rev.,  II  (1913),  138- 


THE  EXISTENCE  OF  A  SUB-ELECTRON?        167 

size.1  The  only  possible  interpretation  then  which  could 
be  put  on  these  two  particles  which  yielded  correct  values 
of  Ne,  but  too  slow  rates  of  fall,  was  that  which  I  put 
upon  them,  namely,  that  they  were  not  spheres  of  oil. 

As  to  the  Vienna  data  on  mercury  and  gold,  Ehren- 
haft  publishes,  all  told,  data  on  just  sixteen  particles  and 
takes  for  his  Brownian-movement  calculations  on  the 
average  fifteen  times  of  fall  and  fifteen  of  rise  on  each,  the 
smallest  number  being  6  and  the  largest  2J.  He  then  com- 
putes his  statistical  average  (A/)2  from  observations  of 
this  sort.  Next  he  assumes  Perrin's  value  of  N,  namely, 
yoXio22,  which  corresponds  to  0  =  4.1,  and  obtains 
instead  by  the  Brownian-movement  method,  i.e.,  the 
Ne  method,  the  following  values  of  e,  the  exponential 
term  being  omitted  for  the  sake  of  brevity:  1.43,  2. 13, 
i .  38,  3 . 04,  3 .  5,  6 . 92,  4 . 42,  3 .  28,  .84.  Barring  the  first 
three  and  the  last  of  these,  the  mean  value  of  e  is  just 
about  what  it  should  be,  namely,  4.22  instead  of  4.  i. 
Further,  the  first  three  particles  are  the  heaviest  ones, 
the  first  one  falling  between  his  cross-hairs  in  3 . 6  seconds, 
and  its  fluctuations  in  time  of  fall  are  from  3.2  to  3.85 
seconds,  that  is,  three-tenths  of  a  second  on  either  side 
of  the  mean  value.  Now,  these  fluctuations  are  only 
slightly  greater  than  those  which  the  average  observer  will 
make  in  timing  the  passage  of  a  uniformly  moving  body 
across  equally  spaced  cross-hairs.  This  means  that  in 
these  observations  two  nearly  equally  potent  causes  were 
operating  to  produce  fluctuations.  The  observed  A/'s 
were,  of  course,  then,  larger  than  those  due  to  Brownian 
movements  alone,  and  might  easily,  with  but  a  few 
observations,  be  two  or  three  times  as  Jarge.  Since 

1  See  Phys.  Rev.,  II  (1913),  134-35- 


i68  THE  ELECTRON 

(A/)2  appears  in  the  denominator  of  equation  (29),  it  will 
be  seen  at  once  that  because  of  the  observer's  timing 
errors  a  series  of  observed  A/'s  will  always  tend  to  be 
larger  than  the  A/  due  to  Brownian  movements  alone, 
and  hence  that  the  Brownian-movement  method  always 
tends  to  yield  too  low  a  value  of  Ne,  and  accordingly 
too  low  a  value  of  e.  It  is  only  when  the  observer's  mean 
error  is  wholly  negligible  in  comparison  with  the  Brownian- 
movement  fluctuations  that  this  method  will  not  yield  too 
low  a  value  of  e.  The  overlooking  of  this  fact  is,  in  my 
judgment,  one  of  the  causes  of  the  low  values  of  e 
recorded  by  Ehrenhaft. 

Again,  in  the  original  work  on  mercury  droplets 
which  I  produced  both  by  atomizing  liquid  mercury  and 
by  condensing  the  vapor  from  boiling  mercury,1 1  noticed 
that  such  droplets  evaporated  for  a  time  even  more 
rapidly  than  oil,  and  other  observers  who  have  since 
worked  with  mercury  have  reported  the  same  behavior.2 
The  amount  of  this  effect  may  be  judged  from  the  fact 
that  one  particular  droplet  of  mercury  recently  under 
observation  in  this  laboratory  had  at  first  a  speed  of 
i  cm.  in  20  seconds,  which  changed  in  half  an  hour  to 
i  cm.  in  56  seconds.  The  slow  cessation,  however,  of 
this  evaporation  indicates  that  the  drop  slowly  becomes 
coated  with  some  sort  of  protecting  film.  Now,  if  any 
evaporation  whatever  is  going  on  while  successive  times 
of  fall  are  being  observed — and  as  a  matter  of  fact 
changes  due  to  evaporation  or  condensation  are  always 
taking  place  to  some  extent — the  apparent  (A/)2  will  be 
larger  than  that  due  to  Brownian  movements,  even 

'  Phys.  Rev.,  XXXII  (1911),  389. 

2  See  Schidlof  et  Karpowicz,  Comples  rendus,  CLVIII  (1914),  1912. 


THE  EXISTENCE  OF  A  SUB-ELECTRON  ?        169 

though  these  movements  are  large  enough  to  prevent  the 
observer  from  noticing,  in  taking  twenty  or  thirty  read- 
ings, that  the  drop  is  continually  changing.  These 
changes  combined  with  the  fluctuations  in  t  due  to  the 
observer's  error  are  sufficient,  I  think,  to  explain  all  of  the 
low  values  of  e  obtained  by  Ehrenhaft  by  the  Brownian- 
movement  method.  Indeed,  I  have  myself  repeatedly 
found  Ne  coming  out  less  than  half  of  its  proper  value 
until  I  corrected  for  the  evaporation  of  the  drop,  and  this 
was  true  when  the  evaporation  was  so  slow  that  its  rate 
of  fall  changed  but  i  or  2  per  cent  in  a  half-hour.  But 
it  is  not  merely  evaporation  which  introduces  an  error 
of  this  sort.  The  running  down  of  the  batteries,  the 
drifting  of  the  drop  out  of  focus,  or  anything  which 
causes  changes  in  the  times  of  passage  across  the  equally 
spaced  cross-hairs  tends  to  decrease  the  apparent  value 
of  Ne.  There  is,  then,  so  far  as  I  can  see,  no  evidence 
at  all  in  any  of  the  data  published  to  date  that  the 
Brownian-movement  method  actually  does  yield  too 
low  a  value  of  e,  and  very  much  positive  evidence  that 
it  does  not  was  given  in  the  preceding  chapter. 

Konstantinowsky's  data  are  very  much  like  Ehren- 
haft's  in  the  possibility  which  they  permit  of  too  low 
values  of  Ne  due  to  observational  error,  evaporation,  and 
drifting  out  of  focus,  but  they  emphasize  one  further 
source  of  error  which  apparently  leads  the  author  en- 
tirely astray.  He  publishes  Ne  observations  on  only  n 
particles,1  five  of  which  yield  values  of  e  between  3 . 3  and 
4.2Xio~10,  or  roughly  correct  values  when  the  fact  is 
considered  that  his  chosen  value  of  N  is  yoXio22;  three 
of  the  others  yield  about  2Xio~10,  two  more  about 

1  Ann.  d.  Phys.,  XL VI  (1915),  292. 


i  yo  THE  ELECTRON 

i  X  io~10,  while  one  yields .  5  X  io~10.  His  determination 
of  the  series  of  multiple  relationships  by  which  he  gets 
the  greatest  common  divisor  (fli+fl2)0  (see  equation  (29) )  is 
however  so  unreliable  that  he  raises  a  question  as  to 
whether  there  is  any  greatest  common  divisor  at  all,  in 
spite  of  the  fact  that  all  other  observers,  a  dozen  of  us 
now  at  least,  including  Ehrenhaft  himself,  now  find  these 
exact  multiple  relations  invariably  to  hold.  But  an 
uncertainty  in  (»x+%)0  (see  equation  (29) )  means  an  equal 
uncertainty  in  Ne.  Konstantinowsky's  very  low  values 
of  Ne  (one-tenth  of  the  normal  value)  are,  then,  in  my 
judgment,  due  to  the  fact  that  he  chooses  the  wrong 
value  of  (fli+z^o-  But  with  apparatus  of  his  dimensions 
and  particles  as  minute  as  he  uses  it  is  not  at  all  sur- 
prising that  he  cannot  find  the  greatest  common  divisor 
of  the  series  of  speeds.  //  would  take  more  observations 
than  he  usually  makes  on  a  particle  to  locate  it  with  cer- 
tainty where  the  Brownian  movements  are  as  large  as  those 
which  his  particles  ought  to  show,  and  where  the  field 
strengths  are  as  small  as  those  which  he  uses  (nine  volts 
only  in  some  cases  on  condenser  plates  2  mm.  apart),  and 
hence  where  the  drops  are  relatively  heavily  charged. 

That  e  and  a  computed  from  the  law  of  fall  become 
farther  and  farther  removed  from  the  values  of  e  and  a 
computed  from  the  Brownian  movements,  the  smaller 
these  particles  appear  to  be,  is  just  what  would  be 
expected  if  the  particles  under  consideration  have  surface 
impurities  or  non-spherical  shapes  or  else  are  not  mer- 
cury at  all.  Again,  the  fact  that  these  data  are  all  taken 
when  the  observers  are  working  with  the  exceedingly 
dense  substances,  mercury  and  gold,  volatilized  in  an 
electric  arc,  and  when,  therefore,  anything  not  mercury  or 


THE  EXISTENCE  OF  A  SUB-ELECTRON?        171 

gold,  but  assumed  to  be,  would  yield  very  low  values  of 
e  and  a,  is  in  itself  a  very  suspicious  circumstance.  The 
further  fact  that  Ehrenhaft  implies  that  normal  values 
of  e  very  frequently  appear  in  his  work,1  while  these 
low  erratic  drops  represent  only  a  part  of  the  data  taken, 
is  suggestive.  When  one  considers,  too,  that  in  place  of 
the  beautiful  consistency  and  duplicability  shown  in  the 
oil-drop  work,  Ehrenhaft  and  his  pupils  never  publish 
data  on  any  two  particles  which  yield  the  same  value 
of  e,  but  instead  find  only  irregularities  and  erratic 
behavior,2  just  as  they  would  expect  to  do  with  non- 
uniform  particles,  or  with  particles  having  dust  specks 
attached  to  them,  one  wonders  why  any  explanation 
other  than  the  foreign-material  one,  which  explains  all 
the  difficulties,  has  ever  been  thought  of.  As  a  matter 
of  fact,  in  our  work  with  mercury  droplets  at  the  Ryerson 
Laboratory,  we  have  found  that  the  initial  rapid  evapo- 
ration gradually  ceases,  just  as  though  the  droplets  had. 
become  coated  with  some  foreign  film  which  prevents 
further  loss.  Schidlof  and  Karpowicz  find  that  the 
behavior  of  their  mercury  drops  as  regards  evaporation 
is  the  same  in  the  purest  nitrogen  as  it  is  in  air.  Ehren- 
haft himself,  in  speaking  of  the  Brownian  movements  of 
his  metal  particles,  comments  on  the  fact  that  they  seem 
at  first  to  show  large  movements  which  grow  smaller  with 

1 "  Die  bei  grosseren  Partikeln  unter  gewissen  Umstanden  bei 
gleicher  Art  der  Erzeugung  haufig  wiederkehrenden  hoheren  Qu'anten 
waren  dann  etwa  als  stabilere  raumliche  Gleichgewichtsverteilungen 
dieser  Sub-electron  anzusehen,  die  sich  unter  gewissen  Umstanden 
ergeben."— Wien.  Ber.,  CXXIII,  59. 

2  Their  whole  case  is  summarized  in  the  tables  in  Ann.  d.  Phys., 
XLIV  (1914),  693,  and  XLVI  (1915),  292,  and  it  is  recommended  that 
all  interested  in  this  discussion  take  the  time  to  glance  at  the  data  on 
these  pages,  for  the  data  themselves  are  so  erratic  as  to  render  dis- 
cussion needless. 


172  THE  ELECTRON 

time.1     This  is  just  what  would  happen  if  the  radius  were 
increased  by  the  growth  of  a  foreign  film. 

Now  what  does  Ehrenhaft  say  to  these  very  obvious 
suggestions  as  to  the  cause  of  his  troubles  ?  Merely  that 
he  has  avoided  all  oxygen,  and  hence  that  an  oxide  film  is 
impossible.  Yet  he  makes  his  metal  particle  by  striking 
an  electric  arc  between  metal  electrodes.  This,  as  everyone 
knows,  brings  out  all  sorts  of  occluded  gases.  Besides, 
chemical  activity  in  the  electric  arc  is  tremendously 
intense,  so  that  there  is  opportunity  for  the  formation  of 
all  sorts  of  higher  nitrites,  the  existence  of  which  in  the 
gases  coming  from  electric  arcs  has  many  times  actually 
been  proved.  Ehrenhaft  says  further  that  he  photographs 
big  mercury  droplets  and  finds  them  spherical  and  free 
from  oxides.  But  the  fact  that  some  drops  are  pure  mer- 
cury is  no  reason  for  assuming  that  all  of  them  are,  and  it 
is  only  the  data  on  those  which  are  not  which  he  publishes. 
Further,  because  big  drops  which  he  can  see  and  measure 
are  of  mercury  is  no  justification  at  all  for  assuming  that 
sub-microscopic  particles  are  necessarily  also  spheres  of 
pure  mercury.  In  a  word,  Ehrenhaft's  tests  as  to 
sphericity  and  purity  are  all  absolutely  worthless  as 
applied  to  the  particles  in  question,  which  according  to 
him  have  radii  of  .the  order  io~6  cm. — a  figure  a  hundred 
times  below  the  limit  of  sharp  resolution. 

IV.      THE  BEARING  OF  THE  VIENNA  WORK  ON  THE  QUES- 
TION  OF   THE   EXISTENCE   OF   A    SUB-ELECTRON 

But  let  us  suppose  that  these  observers  do  actually 
work  with  particles  of  pure  mercury  and  gold,  as  they 

1  "Wie  ich  in  meinen  friiheren  Publikationen  erwahnt  habe  zeigen 
die  ultramikroskopischen  Metallpartikel,  unmittelbar  nach  der  Erzeu- 
gung  beobachtet  eine  viel  lebhaftere  Brownsche  Bewegung  als  nach 
einer  halben  Stunde."— Phys.  Zeiischr.,  XII,  98. 


THE  EXISTENCE  OF  A  SUB-ELECTRON?        173 

think  they  do,  and  that  the  observational  and  evapo ra- 
tional errors  do  not  account  for  the  low  values  of  Ne. 
Then  what  conclusion  could  legitimately  be  drawn  from 
their  data?  Merely  this  and  nothing  more,  that 
(i)  Einstein's  Brownian-movement  equation  is  not  uni- 
versally applicable,  and  (2)  that  the  law  of  motion  of 
their  very  minute  charged  particles  through  air  is  not 
yet  fully  known.  So  long  as  they  find  exact  multiple 
relationships,  as  Ehrenhaft  now  does,  between  the 
charges  carried  by  a  given  partible  when  its  charge  is 
changed  by  the  capture  of  ions  or  the  direct  loss  of  elec- 
trons, the  charges  on  these  ions  must  be  the  same  as  the 
ionic  charges  which  I  have  accurately  and  consistently 
measured  and  found  equal  to  4.77Xio~10  electrostatic 
units;  for  they,  in  their  experiments,  capture  exactly  the 
same  sort  of  ions,  produced  in  exactly  the  same  way  as 
those  which  I  captured  and  measured  in  my  experiments. 
That  these  same  ions  have  one  sort  of  a  charge  when 
captured  by  a  big  drop  and  another  sort  when  captured 
by  a  little  drop  is  obviously  absurd.  //  they  are  not  the 
same  ions  which  are  caught,  then  in  order  to  reconcile  the 
results  with  the  existence  of  the  exact  multiple  relationship 
found  by  Ehrenhaft  as  well  as  ourselves,  it  would  be  neces- 
sary to  assume  that  there  exist  in  the  air  an  infinite  number 
of  different  kinds  of  ionic  charges  corresponding  to  the 
infinite  number  of  possible  radii  of  drops,  and  that  when 
a  powerful  electric  field  drives  all  of  these  ions  toward  a 
given  drop  this  drop  selects  in  each  instance  just  the  charge 
which  corresponds  to  its  particular  radius.  Such  an 
assumption  is  not  only  too  grotesque  for  serious  con- 
sideration, but  it  is  directly  contradicted  by  my  experi- 
ments, for  I  have  repeatedly  pointed  out  that  with  a 


174-  THE  ELECTRON 

given  value  of  -  I  obtain  exactly  the  same  value  of  ely 
whether  I  work  with  big  drops  or  with  little  ones. 

V.   NEW  PROOF  OF  THE  CONSTANCY  OF  6 

For  the  sake  of  subjecting  the  constancy  of  c  to  the 
most  searching  test,  I  have  recently  made  new  measure- 
ments of  the  same  kind  as  those  heretofore  reported,  but 
using  now  a  range  of  sizes  which  overlaps  that  in  which 
Ehrenhaft  works.  I  have  also  varied  through  wide 
limits  the  nature  and^  density  of  both  the  gas  and  the 
drops.  Fig.  13  (I)  contains  new  oil-drop  data  taken  in  air ; 
Fig.  13  (II)  similar  data  taken  in  hydrogen.  The  radii  of 
these  drops,  computed  by  the  very  exact  method  given 
in  the  Physical  Review,1  vary  tenfold,  namely,  from 
.000025  cm.  to  .00023  cm.  Ehrenhaft's  range  is  from 
.000008  cm.  to  .000025  cm.  It  will  be  seen  that  these 
drops  fall  in  every  instance  on  the  lines  of  Fig.  13, 
I  and  II,  and  hence  that  they  all  yield  exactly  the  same 
value  of  el,  namely,  6i.iXio~8.  The  details  of  the 
measurements,  which  are  just  like  those  previously  given, 
will  be  entirely  omitted,  but  sample  data  on  four  of  the 
drops  in  hydrogen  are  given  in  Tables  I,  II,  III,  and  IV, 
above.  There  is  here  not  a  trace  of  an  indication  that  the 
value  of  "e"  becomes  smaller  as  "a"  decreases.  The  points 
on  these  two  curves  represent  consecutive  series  of  obser- 
vations, not  a  single  drop  being  omitted  in  the  case  of 
either  the  air  or  the  hydrogen.  This  shows  the  complete 
uniformity  and  consistency  which  we  have  succeeded  in 
obtaining  in  the  work  with  oil  drops. 

That  mercury  drops  show  a  similar  behavior  was 
somewhat  imperfectly  shown  in  the  original  observations 

'II  (1913),  117. 


THE  EXISTENCE  OF  A  SUB-ELECTRON  ?        175 


176  THE  ELECTRON 

which  I  published  on  mercury.1  I  have  since  fully  con- 
firmed the  conclusions  there  reached.  That  mercury 
drops  can  with  suitable  precautions  be  made  to  behave 
practically  as  consistently  as  oil  is  shown  in  Fig.  13  (III), 
which  represents  data  obtained  by  blowing  into  the 
observing  chamber  above  the  pinhole  in  the  upper  plate  a 
cloud  of  mercury  droplets  formed  by  the  condensation 
of  the  vapor  arising  from  boiling  mercury.  These  results 
have  been  obtained  in  the  Ryerson  Laboratory  with 
my  apparatus  by  Mr.  John  B.  Derieux.  Since  the 
pressure  was  here  always  atmospheric,  the  drops 
progress  in  the  order  of  size  from  left  to  right,  the 
largest  having  a  diameter  about  three  times  that  of 
the  smallest,  the  radius  of  which  is  .00003244  cm. 
The  original  data  may  be  found  in  the  Physical 
Review,  December,  1916.  In  Fig.  13  (IV)  is  found 
precisely  similar  data  taken  with  my  apparatus  by 
Dr.  J.  Y.  Lee  on  solid  spheres  of  shellac  falling 
in  air.2 

These  results  establish  with  absolute  collusiveness  the 
correctness  of  the  assertion  that  the  apparent  value  of  the 
electron  is  not  in  general  a  function  of  the  gas  in  which  the 
par  tide  falls,  of  the  materials  used,  or  of  the  radius  of  the  drop 
on  which  it  is  caught,  even  when  that  drop  is  of  mercury, 
and  even  when  it  is  as  small  as  some  of  those  with  which 
Ehrenhaft  obtained  his  erratic  results.  If  it  appears  to 

lPhys.  Rev.,  CCC  (1911),  389-90. 

a  The  results  shown  in  Fig.  13  do  not  lay  claim  to  the  precision 
reached  in  those  recorded  in  Table  X  and  Fig.  10.  No  elaborate  pre- 
cautions were  here  taken  in  the  calibration  of  the  Hipp  chronoscope  and 
the  voltmeter,  and  it  is  due  to  slight  errors  discovered  later  in  these 
calibrations  that  the  slope  of  line  I  in  Fig.  13  is  not  quite  in  agreement 
with  the  slope  in  Fig.  10. 


THE  EXISTENCE  OF  A  SUB -ELECTRON  ?        177 

be  so  with  his  drops,  the  cause  cannot  possibly  be  found 
in  actual  fluctuations  in  the  charge  of  the  electron  with- 
out denying  completely  the  validity  df  my  results.  But 
these  results  have  now  been  checked,  in  their  essential 
aspects,  by  scores  of  observers,  including  Professor 
Ehrenhaft  himself.  Furthermore,  it  is  not  my  results 
alone  with  which  Ehrenhaft 's  contention  clashes.  The 
latter  is  at  variance  also  with  all  experiments  like  those 
of  Rutherford  and  Geiger  and  Regener  on  the  measure- 
ment -of  the  charges  carried  by  a-  and  /3-particles,  for 
these  are  infinitely  smaller  than  any  particles  used  by 
Ehrenhaft;  and  if,  as  he  contends,  the  value  of  the  unit 
out  of  which  a  charge  is  built  up  is  smaller  and  smaller 
the  smaller  the  capacity  of  the  body  on  which  it  is  found, 
then  these  a-particle  charges  ought  to  be  extraordinarily 
minute  in  comparison  with  the  charges  on  our  oil  drops. 
Instead  of  this,  the  charge  on  the  a-particle  comes  out 
exactly  twice  the  charge  which  I  measure  in  my  oil-drop 
experiments. 

While  then  it  would  not  be  in  keeping  with  the  spirit 
or  with  the  method  of  modern  science  to  make  any  dog- 
matic assertion  about  the  existence  or  non-existence  of  a 
sub-electron,  it  can  be  asserted  with  entire  confidence 
that  there  is  not  in  Ehrenhaft's  experiments  a  scrap  of 
evidence  for  the  existence  of  charges  smaller  than  the 
electron.  If  all  of  his  assumptions  as  to  the  nature  of 
his  particles  are  correct,  then  his  experiments  mean 
simply  that  Einstein's  Brownian-movement  equation  is 
not  of  universal  validity  and  that  the  law  of  motion  of 
minute  charged  particles  is  quite  different  from  that 
which  he  has  assumed.  It  is  very  unlikely  that  either 
of  these  results  can  be  drawn  from  his  experiments,  for 


178  THE  ELECTRON 

Nordlund1  and  Westgren2  have  apparently  verified  the 
Einstein  equation  in  liquids  with  very  much  smaller  par- 
ticles than  Ehrenhaft  uses;  and,  on  the  other  hand,  while 
I  have  worked  with  particles  as  small  as  2X  io~s  cm.  and 

with  values  of  -  as  large  as  135,  which  is  very  much 

larger  than  any  which  appear  in  the  work  of  Ehrenhaft 
and  his  pupils,  I  have  thus  far  found  no  evidence  of  a 
law  of  motion  essentially  different  from  that  which  I 
published  in  1913. 

There  has  then  appeared  up  to  the  present  time  no  evi- 
dence whatever  of  the  existence  of  a  sub-electron. 

1  Zeit.fiir  Phys.  Chem.,  LXXXVII  (1914),  40. 

2  Inaugural  Dissertation  von  Arne  Westgren,  Untersuchungen  uber 
Brownsche  Bewegung,  Stockholm,  1915. 


CHAPTER  IX 
THE  STRUCTURE  OF  THE  ATOM 

We  have  shown  in  the  preceding  chapters  how  within 
the  last  two  decades  there  has  been  discovered  beneath 
the  nineteenth-century  world  of  molecules  and  atoms  a 
wholly  new  world  of  electrons,  the  very  existence  of 
which  was  undreamed  of  twenty  years  ago.  We  have 
seen  that  these  electrons,  since  they  can  be  detached  by 
X-rays  from  all  kinds  of  neutral  atoms,  must  be  con- 
stitu tents  of  all  atoms.  Whether  or  not  they  are  the  sole 
constituents  we  have  thus  far  made  no  attempt  to  deter- 
mine. We  have  concerned  ourselves  with  studying  the 
properties  of  these  electrons  themselves  and  have 
found  that  they  are  of  two  kinds,  negative  and  positive, 
which  are,  however,  exactly  alike  in  strength  of  charge 
but  wholly  different  in  inertia  or  mass,  the  negative  being 
commonly  associated  with  a  mass  which  is  but  1/1,845 
of  that  of  the  lightest  known  atom,  that  of  hydrogen, 
while  the  positive  appears  never  to  be  associated  with 
a  mass  smaller  than  that  of  the  hydrogen  atom.  We 
have  found  how  to  isolate  and  measure  accurately  the 
electronic  charge  and  have  found  that  this  was  the  key 
which  unlocked  the  door  to  many  another  otherwise 
inaccessible  physical  magnitude.  It  is  the  purpose  of 
this  chapter  to  consider  certain  other  fields  of  exact 
knowledge  which  have  been  opened  up  through  the 
measurement  of  the  electron,  and  in  particular  to  discuss 
what  the  physicist,  as  he  has  peered  with  his  newly  dis- 
covered agencies,  X-rays,  radioactivity,  ultra-violet 

179 


iSo  THE  ELECTRON 

light,  etc.,  into  the  insides  of  atoms,  has  been  able  to 
discover  regarding  the  numbers  and  sizes  and  relative 
positions  of  these  electronic  constituents,  and  to  show 
how  far  he  has  gone  in  answering  the  question  as  to 
whether  the  electrons  are  the  sole  building-stones  of 
the  atoms. 

I.      THE   SIZES   OF  ATOMS 

One  of  the  results  of  the  measurement  of  the  electronic 
charge  was  to  make  it  possible  to  find  the  quantity  which 
is  called  the  diameter  of  an  atom  with  a  definiteness  and 
precision  theretofore  altogether  unattained. 

It  was  shown  in  chap,  v  that  the  determination  of  e 
gave  us  at  once  a  knowledge  of  the  exact  number  of 
molecules  in  a  cubic  centimeter  of  a  gas.  Before  this 
was  known  we  had  fairly  satisfactory  information  as  to 
the  relative  diameters  of  different  molecules,  for  we 
have  known  for  a  hundred  years  that  different  gases 
when  at  the  same  temperature  and  pressure  possess  the 
same  number  of  molecules  per  cubic  centimeter  (Avo- 
gadro's  rule).  From  this  it  is  at  once  evident  that,  as 
the  molecules  of  gases  eternally  dart  hither  and  thither 
and  ricochet  against  one  another  and  the  walls  of  the 
containing  vessel,  the  average  distance  through  which 
one  of  them  will  go  between  collisions  with  its  neighbors 
will  depend  upon  how  big  it  is.  The  larger  the  diameter 
the  less  will  be  the  mean  distance  between  collisions— a 
quantity  which  is  technically  called  "the  mean  free  path." 
Indeed,  it  is  not  difficult  to  see  that  in  different  gases  the 
mean  free  path  /  is  an  inverse  measure  of  the  molecular 
cross-section.  The  exact  relation  is  easily  deduced  (see 
Appendix  E).  It  is 

..(31) 


THE  STRUCTURE  OF  THE  ATOM      181 

in  which  d  is  the  molecular  diameter  and  n  is  the  number 
of  molecules  per  cubic  centimeter  of  the  gas.  Now,  we 
have  long  had  methods  of  measuring  /,  for  it  is  upon 
this  that  the  coefficient  of  viscosity  of  the  gas  largely 
depends.  When,  therefore,  we  have  measured  the 
viscosities  of  different  gases  we  can  compute  the  corre- 
sponding Ts,  and  then  from  equation  (31)  the  relative 
diameters  d,  since  n  is  the  same  for  all  gases  at  the  same 
temperature  and  pressure.  But  the  absolute  value  of 
d  can  be  found  only  after  the  absolute  value  of  n  is 
known.  If  we  insert  in  equation  (31)  the  value  of  n 
found  from  e  by  the  method  presented  in  chap,  v,  it  is 
found  that  the  average  diameter  of  the  atom  of  the 
monatomic  gas  helium  is  2Xio~8  cm.,  that  of  the  dia- 
tomic hydrogen  molecule  is  a  trifle  more,  while  the  diam- 
eters of  the  molecules  of  the  diatomic  gases,  oxygen  and 
nitrogen,  are  50  per  cent  larger.1  This  would  make  the 
diameter  of  a  single  atom  of  hydrogen  a  trifle  smaller, 
and  that  of  a  single  atom  of  oxygen  or  nitrogen  a  trifle 
larger  than  that  of  helium.  By  the  average  molecular 
diameter  we  mean  the  average  distance  to  which  the 
centers  of  two  molecules  approach  one  another  in  such 
impacts  as  are  continually  occurring  in  connection  with 
the  motions  of  thermal  agitation  of  gas  molecules — this 
and  nothing  more. 

As  will  presently  appear,  the  reason  that  two  mole- 
cules thus  rebound  from  one  another  when  in  their 
motion  of  thermal  agitation  their  centers  of  gravity  ap- 
proach to  a  distance  of  about  2X  io"8  cm.  is  presumably 
that  the  atom  is  a  system  with  negative  electrons  in  its 
outer  regions.  When  these  negative  electrons  in  two 

'  R.  A.  Millikan,  Phys.  Rev.,  XXXII  (1911),  397. 


182  THE  ELECTRON 

different  systems  which  are  coming  into  collision  ap- 
proach to  about  this  distance,  the  repulsions  between 
these  similarly  charged  bodies  begin  to  be  felt,  although 
at  a  distance  the  atoms  are  forceless.  With  decreasing 
distance  this  repulsion  increases  very  rapidly  until  it 
becomes  so  great  as  to  overcome  the  inertias  of  the 
systems  and  drive  them  asunder. 

II.   THE  RADIUS  OF  THE  ELECTRON  FROM  THE  ELECTRO- 
MAGNETIC THEORY  OF  THE  ORIGIN  OF  MASS 

The  first  estimates  of  the  volume  occupied  by  a 
single  one  of  the  electronic  constituents  of  an  atom  were 
obtained  from  the  electromagnetic  theory  of  the  origin 
of  mass,  and  were  therefore  to  a  pretty  large  degree 
•speculative,  but  since  these  estimates  are  strikingly  in 
accord  with  results  which  follow  from  direct  experiments 
and  are  independent  of  any  theory,  and  since,  further, 
they  are  of  extraordinary  philosophic  as  well  as  historic 
interest,  they  will  briefly  be  presented  here. 

Since  Rowland  proved  that  an  electrically  charged 
body  in  motion  is  an  electrical  current  the  magnitude 
of  which  is  proportional  to  the  speed  of  motion  of  the 
charge,  and  since  an  electric  current,  by  virtue  of  the 
property  called  its  self-induction,  opposes  any  attempt 
to  increase  or  diminish  its  magnitude,  it  is  clear  that  an 
electrical  charge,  as  such,  possesses  the  property  of 
inertia.  But  inertia  is  the  only  invariable  property 
of  matter.  It  is  the  quantitative  measure  of  matter, 
and  matter  quantitatively  considered  is  called  mass.  It 
is  clear,  then,  theoretically,  that  an  electrically  charged 
pith  ball  must  possess  more  mass  than  the  same  pith 
ball  when  uncharged.  But  when  we  compute  how  much 


THE  STRUCTURE  OF  THE  ATOM      183 

the  mass  of  a  pith  ball  is  increased  by  any  charge  which 
we  can  actually  get  it  to  hold,  we  find  that  the  increase 
is  so  extraordinarily  minute  as  to  be 'hopelessly  beyond 
the  possibility  of  experimental  detection.  However, 
the  method  of  making  this  computation,  which  was  first 
pointed  out  by  Sir  J.  J.  Thomson  in  i88i,x  is  of  unques- 
tioned validity,  so  that  we  may  feel  quite  sure  of  the 
correctness  of  the  result.  Further,  when  we  combine 
the  discovery  that  an  electric  charge  possesses  the  dis- 
tinguishing property  of  matter,  namely,  inertia,  with 
the  discovery  that  all  electric  charges  are  built  up  out 
of  electrical  specks  all  alike  in  charge,  we  have  made  it 
entirely  legitimate  to  consider  an  electric  current  as  the 
passage  of  a  definite,  material,  granular  substance  along 
the  conductor.  In  other  words,  the  two  entities,  elec- 
tricity and  matter,  which  the  nineteenth  century  tried 
to  keep  distinct,  bjegin  to  look  like  different  aspects  of 
one  and  the  same  thing. 

But,  though  we  have  thus  justified  the  statement 
that  electricity  is  material,  have  we  any  evidence  as  yet 
that  all  matter  is  electrical — that  is,  that,  all  inertia  is 
of  the  same  origin  as  that  of  an  electrical  charge  ?  The 
answer  is  that  we  have  evidence,  but  as  yet  no  proof. 
The  theory  that  this  is  the  case  is  still  a  speculation, 
but  one  which  rests  upon  certain  very  significant  facts. 
These  facts  are  as  follows: 

If  a  pith  ball  is  spherical  and  of  radius  a,  then  the 
mass  m  due  to  a  charge  E  spread  uniformly  over  its  sur- 
face is  given,  as  is  shown  in  Appendix  D  by, 

2E2 

m—~a  ; (32) 

1  J.  J.  Thomson,  Phil.  Mag.,  XI  (1881),  229. 


184  THE  ELECTRON 

The  point  of  especial  interest  in  this  result  is  that  the 
mass  is  inversely  proportional  to  the  radius,  so  that  the 
smaller  the  sphere  upon  which  we  can  condense  a  given 
charge  E  the  larger  the  mass  of  that  charge.  If,  then,  we 
had  any  means  of  measuring  the  minute  increase  in  mass 
of  a  pith  ball  when  we  charge  it  electrically  with  a  known 
quantity  of  electricity  E,  we  could  compute  from  equation 
(32)  the  size  of  this  pith  ball,  even  if  we  could  not  see 
it  or  measure  it  in  any  other  way.  This  is  much  the  sort 
of  a  position  in  which  we  find  ourselves  with  respect  to 
the  negative  electron.  We  can  measure  its  mass,  and  it  is 
found  to  be  accurately  1/1,845  of  that  of  the  hydrogen 
atom.  We  have  measured  accurately  its  charge  and 
hence  can  compute  the  radius  a  of  the  equivalent  sphere, 
that  is,  the  sphere  over  which  e  would  have  to  be  uni- 
formly distributed  to  have  the  observed  mass,  provided 
we  assume  that  the  observed  mass  of  the  electron  is  all 
due  to  its  charge. 

The  justification  for  such  an  assumption  is  of  two 
kinds.  First,  since  we  have  found  that  electrons  are 
constituents  of  all  atoms  and  that  mass  is  a  property 
of  an  electrical  charge,  it  is  of  course  in  the  interests 
of  simplicity  to  assume  that  all  the  mass  of  an  atom  is 
due  to  its  contained  electrical  charges,  rather  than  that 
there  are  two  wholly  different  kinds  of  mass,  one  of 
electrical  origin  and  the  other  of  some  other  sort  of  an 
origin.  Secondly,  if  the  mass  of  a  negative  electron 
is  all  of  electrical  origin,  then  we  can  show  from  electro- 
magnetic theory  that  this  mass  ought  to  be  independent 
of  the  speed  with  which  the  electron  may  chance  to  be 
moving  unless  that  speed  approaches  close  to  the  speed 
of  light.  But  from  one-tenth  the  speed  of  light  up  to 


THE  STRUCTURE  OF  THE  ATOM      185 

that  speed  the  mass  ought  to  vary  with  speed  in  a 
definitely  predictable  way. 

Now,  it  is  a  piece  of  rare  good  fortune  for  the  testing 
of  this  theory  that  radium  actually  does  eject  negative 
electrons  with  speeds  which  can  be  accurately  measured 
and  which  do  vary  from  three-tenths  up  to  ninety-eight 
hundredths  of  that  of  light.  //  is  further  one  of  the 
capital  discoveries  of  the  twentieth  century*  that  within 
these  limits  the  observed  rate  of  variation  of  the  mass 
of  the  negative  electron  with  speed  agrees  accurately  with 
the  rate  of  variation  computed  on  the  assumption  that  this 
mass  is  all  of  electrical  origin.  This  leaves  no  room  for  a 
mass  of  any  other  kind  to  be  associated  with  the  free 
negative  electron.  Such  is  the  experimental  argument 
for  the  electrical  origin  of  mass. 

Solving  then  equation  (32)  for  a,  we  find  that  the 
radius  of  the  sphere  over  which  the  charge  e  of  the 
negative  electron  would  have  to  be  distributed  to  have 
the  observed  mass  is  but  2X  io~13  cm.,  or  but  one  fifty- 
thousandth  of  the  radius  of  the  atom  (io~8cm.).  From 
this  point  of  view,  then,  the  negative  electron  represents  a 
charge  of  electricity  which  is  condensed  into  an  exceed- 
ingly minute  volume.  In  fact,  its  radius  cannot  be 
larger  in  comparison  with  the  radius  of  the  atom  than 
is  the  radius  of  the  earth  in  comparison  with  the  radius 
of  her  orbit  about  the  sun. 

In  the  case  of  the  positive  electron  there  is  no  direct 
experimental  justification  for  the  assumption  that  the 
mass  is  also  wholly  of  electrical  origin,  for  we  cannot 
impart  to  the  positive  electrons  speeds  which  approach 
the  speed  of  light,  nor  have  we  as  yet  found  in  nature 

1  Bucherer,  Annalen  der  Physik,  XXVIII  (1909),  513. 


i86  THE  ELECTRON 

any  of  them  which  are  endowed  with  speeds  greater  than 
about  one-tenth  that  of  light.  But  in  view  of  the  experi- 
mental results  obtained  with  the  negative  electron,  the 
carrying  over  of  the  same  assumption  to  the  positive  elec- 
tron is  at  least  natural.  Further,  if  this  step  be  taken, 
it  is  clear  from  equation  (32),  since  m  for  the  positive  is 
nearly  two  thousand  times  larger  than  m  for  the  negative, 
that  a  for  the  positive  can  be  only  1/2,000  of  what  it  is 
for  the  negative.  In  other  words,  the  size  of  the  positive 
electron  would  be  to  the  size  of  the  negative  as  a  sphere 
having  a  two-mile  radius  would  be  to  the  size  of  the 
earth.  From  the  standpoint;  then,  of  the  electromagnetic 
theory  of  the  origin  of  mass,  the  dimensions  of  the 
negative  and  positive  constituents  of  atoms  in  com- 
parison with  the  dimensions  of  the  atoms  themselves  are 
like  the  dimensions  of  the  planets  and  asteroids  in  com- 
parison with  the  size  of  the  solar  system.  All  of  these 
computations,  whatever  their  value,  are  rendered  pos- 
sible by  the  fact  that  e  is  now  known. 

Now  we  know  from  methods  which  have  nothing  to 
do  with  the  electromagnetic  theory  of  the  origin  of 
mass,  that  the  excessive  minuteness  predicted  by  that 
theory  for  both  the  positive  and  the  negative  constitu- 
ents of  atoms  is  in  fact  correct,  though  we  have  no  evi- 
dence as  to  whether  the  foregoing  ratio  is  right. 

III.    DIRECT    EXPERIMENTAL    PROOF    OF    THE    EXCESSIVE 

MINUTENESS   OF   THE  ELECTRONIC  CONSTITUENTS 

OF  ATOMS 

For  more  than  ten  years  we  have  had  direct  experi- 
mental proof1  that  the  fastest  of  the  a-particles,  or 

'  Bragg,  Phil.  Mag.,  VIII  (1904),  719,  726;  X  (1905),  318;  XI 
(1906),  617. 


FIG.  14 


FIG.  15 


PHOTOGRAPHS  OF  THE  TRACKS  OF  CI-PARTICLES 
SHOOTING  THROUGH  AIR 


FIG.  16 


FIG.  17 


PHOTOGRAPHS  OF  THE  TRACKS  OF  /S-PARTICLES 
SHOOTING  THROUGH  AIR 


THE  STRUCTURE  OF  THE  ATOM  187 

helium  atoms,  which  are  ejected  by  radium,  shoot  in 
practically  straight  lines  through  as  much  as  7  cm.  of 
air  at  atmospheric  pressure  before  being  brought  to  rest. 
Some  a-par tides  which  have  a  range  of  11.3  cm.  have 
just  been  found.1  Figs.  14  and  15  show  actual  photo- 
graphs of  the  tracks  of  such  particles.  We  know  too, 
for  the  reasons  given  on  p.  138,  that  these  a-par  tides  do 
not  penetrate  the  air  after  the  manner  of  a  bullet,  namely, 
by  pushing  the  molecules  of  air  aside,  but  rather  that 
they  actually  shoot  through  all  the  molecules  of  air  which 
they  encounter.  The  number  of  such  passages  through 
molecules  which  an  a-particle  would  have  to  make  in 
traversing  seven  centimeters  of  air  would  be  about  half 
a  million. 

Further,  the  very  rapid  /3-particles,  or  negative 
electrons,  which  are  shot  out  by  radium  have  been 
known  for  a  still  longer  time  to  shoot  in  straight  lines 
through  much  greater  distances  in  air  than  7  cm.,  and 
even  to  pass  practically  undeflected  through  appreciable 
thicknesses  of  glass  or  metal. 

We  saw  in  chap,  vi  that  the  tracks  of  both  the  a-  and 
the  /3-particles  through  air  could  be  photographed 
because  they  ionize  some  of  the  molecules  through  which 
they  pass.  These  ions  then  have  the  property  of  con- 
densing water  vapor  about  themselves,  so  that  water 
droplets  are  formed  which  can  be  photographed  by 
virtue  of  the  light  which  they  reflect.  Fig.  17  shows  the 
track  of  a  very  high-speed  /3-ray.  A  little  to  the  right  of 
the  middle  of  the  photograph  a  straight  line  can  be 
drawn  from  bottom  to  top  which  will  pass  through  a 
dozen  or  so  of  pairs  of  specks.  These  specks  are  the 

1  Rutherford  and  Wood,  Phil.  Mag.,  XXXI  (1916),  379. 


1 88  THE  ELECTRON 

water  droplets  formed  about  the  ions  which  were  pro- 
duced at  these  points.  Since  we  know  the  size  of  a 
molecule  and  the  number  of  molecules  per  cubic  centi- 
meter, we  can  compute,  as  in  the  case  of  the  a-particle, 
the  number  of  molecules  through  which  a  /3-particle 
must  pass  in  going  a  given  distance.  The  extraordinary 
situation  revealed  by  this  photograph  is  that  this  par- 
ticular particle  shot  through  on  an  average  as  many  as 
10,000  atoms  before  it  came  near  enough  to  an  elec- 
tronic constituent  of  any  one  of  these  atoms  to  detach 
it  from  its  system  and  form  an  ion.  This  shows  con- 
clusively that  the  electronic  or  other  constituents  of  atoms 
can  occupy  but  an  exceedingly  small  fraction  of  the  space 
inclosed  within  the  atomic  system.  Practically  the  whole 
of  this  space  must  be  empty  to  an  electron  going  with 
this  speed. 

The  left  panel  in  the  lower  half  of  the  plate  (Fig.  16) 
shows  the  track  of  a  negative  electron  of  much  slower 
speed,  and  it  will  be  seen,  first,  that  it  ionizes  much 
more  frequently,  and,  secondly,  that  instead  of  continu- 
ing in  a  straight  line  it  is  deflected  at  certain  points 
from  its  original  direction.  The  reason  for  both  of  these 
facts  can  readily  be  seen  from  the  considerations  on 
p.  138,  which  it  may  be  worth  while  to  extend  to  the  case 
in  hand  as  follows. 

If  a  new  planet  or  other  relatively  small  body  were 
to  shoot  with  stupendous  speed  through  our  solar  sys- 
tem, the  time  which  it  spent  within  our  system  might 
be  so  small  that  the  force  between  it  and  the  earth  or 
any  other  member  of  the  solar  system  would  not  have 
time  either  to  deflect  the  stranger  from  its  path  or  to 
pull  the  earth  out  of  its  orbit.  If  the  speed  of  the  strange 


FIG. 18 


FIG.  19 


FIG.  20 


PHOTOGRAPHS  OF  THE  TRACKS  OF  /S-PARTICLES  EJECTED 
BY  X-RAYS  FROM  MOLECULES  OF  AlR 


THE  STRUCTURE  OF  THE  ATOM      189 

body  were  smaller,  however,  the  effect  would  be  more 
disastrous  both  to  the  constituents  of  our  solar  system 
and  to  the  path  of  the  strange  body,  for  the  latter 
would  then  have  a  much  better  chance  of  pulling  one 
of  the  planets  out  of  our  solar  system  and  also  a 
much  better  chance  of  being  deflected  from  a  straight 
path  itself.  The  slower  a  negative  electron  moves, 
then,  the  more  is  it  liable  to  deflection  and  the  more 
frequently  does  it  ionize  the  molecules  through  which 
it  passes. 

This  conclusion  finds  beautiful  experimental  con- 
firmation in  the  three  panels  of  the  plate  opposite  this 
page,  for  the  speed  with  which  X-rays  hurl  out  negative 
electrons  from  atoms  has  long  been  known  to  be  much 
less  than  the  speed  of  /3-rays  from  radium,  and  the  zigzag 
tracks  in  these  photographs  are  the  paths  of  these  cor- 
puscles. It  will  be  seen  that  they  bend  much  more  often 
and  ionize  much  more  frequently  than  do  the  rays  shown 
in  Figs.  1 6  and  17. 

But  the  study  of  the  tracks  of  the  a-particles  (Figs.  14 
and  15,  opposite  p.  186)  is  even  more  illuminating  as 
to  the  structure  of  the  atom.  For  the  a-particle,  being 
an  atom  of  helium  eight  thousand  times  more  massive 
than  a  negative  electron,  could  no  more  be  deflected  by 
one  of  the  latter  in  an  atom  through  which  it  passes 
than  a  cannon  ball  could  be  deflected  by  a  pea..  Yet 
Figs.  14  and  15  show  that  toward  the  end  of  its  path 
the  a-particle  does  in  general  suffer  several  sudden 
deflections.  Such  deflections  could  be  produced  only 
by  a  very  powerful  center  of  force  within  the  atom 
whose  mass  is  at  least  comparable  with  the  mass  of  the 
helium  atom. 


THE  ELECTRON 

These  sharp  deflections,  which  occasionally  amount 
to  as  much  as  150°  to  180°,  lend  the  strongest  of  support 
to  the  view  that  the  atom  consists  of  a  heavy  positively 
charged  nucleus  about  which  are  grouped  enough  elec- 
trons to  render  the  whole  atom  neutral.  But  the  fact 
that  in  these  experiments  the  a-particle  goes  through 
500,000  atoms  without  approaching  near  enough  to  this 
central  nucleus  to  suffer  appreciable  deflection  more 
than  two  or  three  times  constitutes  the  most  convincing 
evidence  that  this  central  nucleus  which  holds  the  nega- 
tive electrons  within  the  atomic  system  occupies  an 
excessively  minute  volume,  just  as  we  computed  from 
the  electromagnetic  theory  of  the  origin  of  mass  that 
the  positive  electron  ought  to  do.  Indeed,  knowing  as 
he  did  by  direct  measurement  the  speed  of  the  a-particle, 
Rutherford,  who  is  largely  responsible  for  the  nucleus- 
atom  theory,  first  computed,1  with  the  aid  of  the  inverse 
square  law,  which  we  know  to  hold  between  charged 
bodies  of  dimensions  which  are  small  compared  with  their 
distances  apart,  how  close  the  a-particle  would  approach 
to  the  nucleus  of  a  given  atom  like  that  of  gold  before 
it  would  be  turned  back  upon  its  course  (see  Appendix  F). 
The  result  was  in  the  case  of  gold,  one  of  the  heaviest 
atoms,  about  io~"  cm.,  and  in  the  case  of  hydrogen,  the 
lightest  atom,  about  io"13  cm.  These  are  merely  upper 
limits  for  the  dimensions  of  the  nuclei. 

However  uncertain,  then,  we  may  feel  about  the 
sizes  of  positive  and  negative  electrons  computed  from 
the  electromagnetic  theory  of  the  origin  of  the  mass,  we 
may  regard  it  as  fairly  well  established  by  such  direct 
experiments  as  these  that  the  electronic  constituents 

'  Phil.  Mag.,  XXI  (1911),  669. 


THE  STRUCTURE  OF  THE  ATOM      191 

of  atoms  are  as  small,  in  comparison  with  the  dimensions 
of  the  atomic  systems,  as  are  the  sun  and  planets  in 
comparison  with  the  dimensions  of  the  solar  system. 
Indeed,  when  we  reflect  that  we  can  shoot  helium  atoms 
by  the  billion  through  a  thin-walled  highly  evacuated 
glass  tube  without  leaving  any  holes  behind,  i.e.,  without 
impairing  in  the  slightest  degree  the  vacuum  or  percep- 
tibly weakening  the  glass,  we  see  from  this  alone  that 
the  atom  itself  must  consist  mostly  of  "hole";  in  other 
words,  that  an  atom,  like  a  solar  system,  must  be  an 
exceedingly  loose  structure  whose  impenetrable  portions 
must  be  extraordinarily  minute  in  comparison  with  the 
penetrable  portions.  The  notion  that  an  atom  can 
appropriate  to  itself  all  the  space  within  its  boundaries 
to  the  exclusion  of  all  others  is  then  altogether  exploded 
by  these  experiments.  A  particular  atom  can  certainly 
occupy  the  same  space  at  the  same  time  as  any  other 
atom  if  it  is  only  endowed  with  sufficient  kinetic  energy. 
Such  energies  as  correspond  to  the  motions  of  thermal 
agitation  of  molecules  are  not,  however,  sufficient  to 
enable  one  atom  to  penetrate  the  boundaries  of  another, 
hence  the  seeming  impenetrability  of  atoms  in  ordinary 
experiments  in  mechanics.  That  there  is,  however,  a 
portion  of  the  atom  which  is  wholly  impenetrable  to  the 
alpha  particles  is  definitely  proved  by  experiments  of 
the  sort  we  have  been  considering;  for  it  occasionally 
happens  that  an  alpha  particle  hits  this  nucleus  "head 
on,"  and,  when  it  does  so,  it  is  turned  straight  back 
upon  its  course.  As  indicated  above,  the  size  of  this 
impenetrable  portion,  which  may  be  defined  as  the  size 
of  the  nucleus,  is  in  no  case  larger  than  i/ 10,000  the 
diameter  of  the  atom. 


iy2  THE  ELECTRON 

IV.      THE  NUMBER   OF  ELECTRONS  IN  AN  ATOM 

If  it  be  considered  as  fairly  conclusively  established 
by  the  experiments  just  described  that  an  atom  consists 
of  a  heavy  but  very  minute  positively  charged  nucleus 
which  holds  light  negative  electrons  in  some  sort  of  a 
configuration  about  it,  then  the  number  of  negative 
electrons  outside  the  nucleus  must  be  such  as  to  have  a 
total  charge  equal  to  the  free  positive  charge  of  the 
nucleus,  since  otherwise  the  atom  could  not  be  neutral. 

But  the  positive  charge  on  the  nucleus  has  been 
approximately  determined  as  follows:  With  the  aid  of 
the  knowledge,  already  obtained  through  the  determina- 
tion of  e,  of  the  exact  number  of  atoms  in  a  given  weight 
of  a  given  substance,  Sir  Ernest  Rutherford1  first  com- 
puted the  chance  that  a  single  helium  atom  in  being 
shot  with  a  known  speed  through  a  sheet  of  gold  foil 
containing  a  known  number  of  atoms  per  unit  of  area  of 
the  sheet  would  suffer  a  deflection  through  a  given  angle. 
This  computation  can  easily  be  made  in  terms  of  the 
known  kinetic  energy  and  charge  of  the  a-particle, 
the  known  number  of  atoms  in  the  gold  foil,  and  the 
unknown  charge  on  the  nucleus  of  the  gold  atom  (see 
Appendix  F).  Geiger  and  Marsden2  then  actually 
counted  in  Rutherford's  laboratory,  by  means  of  the 
scintillations  produced  on  a  zinc-sulphide  screen,  what 
fraction  of,  say,  a  thousand  a-particles,  which  were 
shot  normally  into  the  gold  foil,  were  deflected  through 
a  given  angle,  and  from  this  observed  number  and 
Rutherford's  theory  they  obtained  the  number  of  free 
positive  charges  on  the  nucleus  of  the  gold  atom. 

'  Phil.  Mag.,  XXI  (1911),  669-88. 

'Ibid.,  XXV  (1913),  604. 


THE  STRUCTURE  OF  THE  ATOM      193 

Repeating  the  experiment  and  the  computations 
with  foils  made  from  a  considerable  number  of  other 
metals,  they  found  that  in  every  case  the  number  of  free 
positive  charges  on  the  atoms  of  different  substances  was 
approximately  equal  to  half  its  atomic  weight.  This 
means  that  the  aluminum  atom,  for  example,  has  a 
nucleus  containing  about  thirteen  free  positive  charges 
and  that  the  nucleus  of  the  atom  of  gold  contains  in 
the  neighborhood  of  a  hundred.  This  result  Was  in 
excellent  agreement  with  the  conclusion  reached  inde- 
pendently by  Barkla1  from  experiments  of  a  wholly 
different  kind,  namely,  experiments  on  the  scattering 
of  X-rays.  These  indicated  that  the  number  of  scatter- 
ing centers  in  an  atom — that  is,  its  number  of  free 
negative  electrons — was  equal  to  about  half  the  atomic 
weight.  But  this  number  must,  of  course,  equal,  the 
number  of  free  positive  electrons  in  the  nucleus. 

v.    MOSELEY'S  REMARKABLE  DISCOVERY 

The  foregoing  result  was  only  approximate.  Indeed, 
there  was  internal  evidence  in  Geiger  and  Marsden's 
work  itself  that  a  half  was  somewhat  too  high:  The 
answer  has  recently  been  made  very  definite  and  very 
precise  through  the  extraordinary  work  of  a  brilliant 
young  Englishman,  Moseley,  who,  at  the  age  of  twenty- 
seven,  had  accomplished  as  notable  a  piece  of  research 
in  physics  as  has  appeared  during  the  last  fifty  years. 
Such  a  mind  has  recently  fallen  a  victim  to  the  most 
ghastly  crime  in  history,  the  present  European  war.  He 
was  shot  and  killed  instantly  in  the  trenches  in  the 
summer  of  1915. 

1  Barkla,  Phil.  Mag.,  XXI  (1911),  648. 


194  THE  ELECTRON 

Laue  in  Munich  had  suggested  in  1912  the  use  of  the 
regular  spacing  of  the  molecules  of  a  crystal  for  the 
analysis,  according  to  the  principle  of  the  grating,  of 
ether  waves  of  very  short  wave-length,  such  as  X-rays 
were  supposed  to  be,  and  the  Braggs1  had  not  only 
perfected  an  X-ray  spectrometer  which  utilized  this 
principle,  but  had  determined  accurately  the  wave- 
lengths of  the  X-rays  which  are  characteristic  of  certain 
metals.  The  accuracy  with  which  this  can  be  done  is 
limited  simply  by  the  accuracy  in  the  determination  of  e, 
so  that  the  whole  new  field  of  exact  X-ray  spectrometry 
is  made  available  through  our  exact  knowledge  of  e. 
Moseley's  discovery,2  made  as  a  result  of  an  elaborate 
and  difficult  study  of  the  wave-lengths  of  the  character- 
istic X-rays  which  were  excited  when  cathode  rays  were 
made  to  impinge  in  succession  upon  anticathodes  em- 
bracing most  of  the  known  elements,  was  that  these 
characteristic  wave-lengths  of  the  different  elements,  or, 
better,  their  characteristic  frequencies,  are  related  in  a 
very  simple  but  a  very  significant  way.  These  frequencies 
were  found  to  constitute  the  same  sort  of  an  arithmetical 
progression  as  do  the  charges  which  we  found  to  exist  on  our 
oil  drops.  It  was  the  square  root  of  the  frequencies  rather 
than  the  frequencies  themselves  which  showed  this  beauti- 
fully simple  relationship,  but  this  is  an  unimportant  detail. 
The  significant  fact  is  that,  arranged  in  the  order  of  increas- 
ing frequency  of  their  characteristic  X-ray  spectra,  all  the 
known  elements  which  have  been  examined  constitute  a 
simple  arithmetical  series  each  member  of  which  is  obtained 
from  its  predecessor  by  adding  always  the  same  quantity. 

1  Bragg,  X-Rays  and  Crystal  Structure,  1915. 

*  Phil.  Mag.,  XXVI  (1912),  1024;  XXVII  (1914),  703. 


.2 
$ 

CO 


THE  STRUCTURE  OF  THE  ATOM  195 

The  plate  opposite  this  page  shows  photographs  of 
the  X-ray  spectra  of  a  number  of  elements  whose  atomic 
numbers — that  is,  the  numbers  assigned  them  in  Mose- 
ley's  arrangement  of  the  elements  on  the  basis  of  increas- 
ing X-ray  frequency — are  given  on  the  left.  These 
photographs  were  taken  by  Siegbahn.1  The  distance 
from  the  " central  image" — in  this  case  the  black  line 
on  the  left — to  a  given  line  of  the  line  spectrum  on  the 
right  is  approximately  proportional  to  the  wave-length 
of  the  rays  producing  this  line.  The  photographs  show 
beautifully,  first,  how  the  atoms  of  all  the  elements 
produce  spectra  of  just  the  same  type,  and,  secondly,  how 
the  wave-lengths  of  corresponding  lines  decrease,  or 
the  frequencies  increase,  with  increasing  atomic  number. 
The  photograph  on  the  left  shows  this  progression  for 
the  highest  frequency  rays  which  the  atoms  produce,  the 
so-called  K  series,  while  the  one  on  the  right  shows  the 
same  sort  of  a  progression  for  the  next  lower  frequency 
rays,  namely,  those  of  the  so-called  L  series,  which  have 
uniformly  from  seven  to  eight  times  the  wave-length 
of  the  K  series.  The  plate  opposite  p.  197  shows  some 
very  beautiful  photographs  taken  by  De  Broglie  in  Paris2 
in  October,  1916.  The  upper  one  is  the  X-ray  emission 
spectrum  of  tungsten.  It  consists  of  general  radia- 
tions, corresponding  to  white  light,  scattered  through- 
out the  whole  length  of  the  spectrum  as  a  background 
and  superposed  upon  this  two  groups  of  lines.  The 
two  K  lines  are  here  close  to  the  central  image,  for 
the  K  wave-lengths  are  here  very  short,  since  tungsten 
has  a  high  atomic  number  (74).  Farther  to  the  right 

1  Jahrbuch  der  Radioaktivitat  u.  Elektronik,  XIII  (1916),  326. 
3  Comptes  rcndus,  CLXV  (1916),  87,  352. 


196  THE  ELECTRON 

is  the  L  series  of  tungsten  lines  which  will  be  recognized 
because  of  its  similarity  to  the  L  series  in  the  plate 
opposite  p.  195.  Between  the  K  and  the  L  lines  are  two 

absorption    edges   marked    j^     and   j^  .     The   former 

represents  the  frequency  above  which  the  silver  absorbs 
all  the  general  radiation  of  tungsten  but  below  which  it 
lets  it  all  through.  The  latter  is  the  corresponding  line 
for  bromine.  In  a  print  from  a  photograph  absorption 
in  the  plate  itself  obviously  appears  as  a  darkening, 
transmission  as  a  lightening.  Just  below  is  the  spectrum 
obtained  by  inserting  a  sheet  of  molybdenum  tn  the 
path  of  the  beam,  i.e.,  before  the  slit  of  the  spectrometer. 
Absorption  in  the  molybdenum  will  obviously  appear 
as  a  lightening,  transmission  as  a  darkening.  It  will 
be  seen  that  the  molybdenum  absorbs  all  the  frequencies 
in  the  X-ray  emission  of  tungsten  higher  than  a  partic- 
ular frequency  and  lets  through  all  frequencies  lower 
than  this  value.  This  remarkable  characteristic  of 
the  absorption  of  X-rays  was  discovered  by  Barkla  in 
I909.1  The  absorption  edge  at  which,  with  increasing 
frequency,  absorption  suddenly  begins  is  very  sharply 
marked.  This  edge  coincides,  as  will  presently  be  shown, 
with  the  highest  emission  frequency  of  which  molyb- 
denum is  capable.  De  Broglie  has  measured  accurately 
these  critical  absorption  frequencies  for  all  the  heavy 
elements  up  to  thorium,  thus  extending  the  K  series 
from  atomic  number  N=  60  where  he  found  it,  to  N=  90, 
a  notable  advance.  The  two  absorption  edges  character- 
istic of  the  silver  and  the  bromine  in  the  photographic 
plate  appear  in  the  same  place  on  all  the  photographs  in 

1  Barkla  and  Sadler,  Phil.  Mag.,  XVII  (May,  1909),  749, 


W        TV,  Br    W      W        W  N«»74 

Ka*«      KA  Kx  Ly  ,    L0        U         N»5'47 


ry  Nz8fl 

FIG.  22.— X-RAY  ABSORPTION  SPECTRA,  K  SERIES 


FIG.  23 — X-RAY  ABSORPTION  SPECTRA,  L  SERIES 


FIG.  24. — HYDROGEN  SPECTRUM  FROM  A  NEBULA 


198 


THE  ELECTRON 


THE  STRUCTURE  OF  THE  ATOM 


199 


with  the  shortest  beta  line  of  this  L  series.  The  other 
absorption  edge  in  the  L  region  also  coincides  in  every 
case  with  an  emission  line,  though  the  data  are  as  yet 
too  meager  to  permit  of  any  general  statement  as  to 
what  this  line  is. 

TABLE  XIV 

COMPARISON  OF  KA  AND  K/s 


N 

Element 

KA 

Ke 

N 

Element 

KA 

K^ 

2C  .    . 

Br 

014 

014 

C2  .  . 

I 

167 

(  380) 

27.    . 

Rb 

810 

8n 

cc  .  . 

Cs 

^8 

340 

2.8  

Sr 

.764 

.767 

•56.  . 

Ba 

2.2C, 

222) 

4O 

Zr 

681 

(  60$) 

C7 

La 

7  TO 

•2  TQ) 

41 

Nb 

6  AC. 

6c.7 

s8 

Ce 

298 

•6^J 
(    3O4.) 

42 

Mo 

611 

(  620) 

78 

Pt 

I  C.O 

46  

Pd 

•  ^o^ 

•   ^O^ 

70.  . 

Au 

•  J47 

47  

Ag 

•479 

.488 

so.  .. 

Hg 

•  143 

48      

Cd 

4.C.8 

(  4.66) 

81 

Tl 

I  3Q 

CQ    . 

Sn 

4.10 

(     4.10) 

82 

Pb 

J  7  C 

CT 

Sb 

2QQ 

408 

8* 

Bi 

I  3.O 

C2.   . 

Te 

381 

(  ^06) 

oo 

Th 

098  about 

COMPARISON  OF  LA  AND  L/s 


N 

Element 

LA 

L* 

N 

Element 

LA 

h 

78      .       .. 

Pt 

I     O67 

I    O72 

OO 

Th 

7S6 

7^O 

70    . 

Au 

I    O37 

I    O3  C. 

02 

u 

7IO 

7O2 

82    

Pb 

04.  r 

O4.8 

Since  these  enormously  high  X-ray  frequencies  are 
presumably  due  to  the  vibrations  arising  from  electrons 
which  are  in  extraordinarily  powerful  fields  of  force,  such 
as  might  be  expected  to  exist  in  the  inner  regions  of  the 
atom  close  to  the  nucleus,  Moseley's  discovery  strongly 
suggests  that  the  charge  on  this  nucleus  is  produced  in  the 
case  of  each  atom  by  adding  some  particular  invariable 


200  THE  ELECTRON 

charge  to  the  nucleus  of  the  atom  next  below  it  in 
Moseley's  table.  This  suggestion  gains  added  weight 
when  it  is  found  that  with  one  or  two  trifling  exceptions, 
to  be  considered  later,  Moseley's  series  of  increasing 
X-ray  frequencies  is  exactly  the  series  of  increasing  atomic 
weights.  It  also  receives  powerful  support  from  the 
following  recent  discovery. 

Mendeleeff's  periodic  table  shows  that  the  progres- 
sion of  chemical  properties  among  the  elements  coincides 
in  general  with  the  progression  of  atomic  weights.  Now 
it  has  recently  been  pointed  out  that  whenever  a  radio- 
active substance  loses  a  doubly  charged  a-particle  it 
moves  two  places  to  the  left  in  the  periodic  table,  while 
whenever  it  loses  a  singly  charged  /3-particle  it  moves 
one  place  to  the  right,1  thus  showing  that  the  chemical 
character  of  a  substance  depends  upon  the  number  of 
free  positive  charges  in  its  nucleus. 

One  of  the  most  interesting  and  striking  character- 
istics of  Moseley's  table  is  that  all  the  known  elements 
between  sodium  (atomic  number  n,  atomic  weight  23) 
and  lead  (atomic  number  82,  atomic  weight,  207.2)  have 
been  fitted  into  it  and  there  are  left  but  four  vacancies 
within  this  range.  Below  sodium  there  are  just  10 
known  elements,  and  the  X-ray  spectra  of  these  have 
not  as  yet  been  obtained,  but  the  progression  of  atomic 
weights  and  of  chemical  properties  is  here  altogether 
definite  and  unambiguous.  It  seems  highly  probable 
then  from  Moseley's  work  that  we  have  already  found 
all  except  four  of  the  complete  series  of  different  types 
of  atoms  from  hydrogen  to  lead,  i.e.,  from  i  to  82,  of 
which  the  physical  world  is  built.  From  82  to  92  comes 

1  Soddy,  The  Chemistry  of  the  Radioelements,  Part  II,  1914. 


THE  STRUCTURE  OF  THE  ATOM      201 

the  group  of  radioactive  elements  which  are  continually 
transmuting  themselves  into  one  another,  and  above  92 
(uranium)  it  is  not  likely  that  any  elements  exist. 

That  hydrogen  is  indeed  the  base  of  the  Moseley 
series  is  rendered  well-nigh  certain  by  the  following 
computation.  If  we  write  Moseley's  discovery  that 
the  square  roots  of  the  highest  frequencies,  n^  n2,  etc., 
emitted  by  different  atoms  are  proportional  to  the 
nuclear  charges,  EI}  £2,  etc.,  in  the  following  form: 

»i=|ior^=i.  ..(33) 


and  substitute  for  X2  the  observed  wave-length  of  the  high- 
est frequency  line  emitted  by  tungsten — a  wave-length 
which  has  been  found  by  Hull  to  be  o.i85Xio~8  cm.; 
and,  further,  if  we  substitute  for  E2,  74,  the  atomic 
number  of  tungsten,  and  for  ET,  i,  we  should  obtain,  by 
solving  for  Xx,  the  wave-length  of  the  highest  frequency 
line  which  can  be  emitted  by  the  element  whose  nucleus 
contains  but  one  single  positive  electron.  The  result  of 
this  substitution  is  Xx=  101 . 3  up  (million ths  millimeters). 
Now  the  wave-length  corresponding  to  the  highest 
frequency  in  the  ultra-violet  series  of  hydrogen  lines 
recently  discovered  by  Lyman  is  91.2/4/4  and  there  is 
every  reason  to  believe  from  the  form  of  the  B aimer  series 
of  which  this  is  the  convergence  wave-length  that  it  cor- 
responds to  the  highest  frequency  of  which  the  hydrogen 
atom  is  capable.  The  agreement  is  only  approximate, 
but  it  is  as  close  as  could  be  expected  in  view  of  the  lack 
of  exact  equality  in  the  Moseley  steps.  //  is  well-nigh 
certain,  then,  that  this  Lyman  ultra-violet  series  of  hydrogen 


202  THE  ELECTRON 

lines  is  nothing  but  the  K  X-ray  series  of  hydrogen. 
Similarly,  it  is  equally  certain  that  the  L  X-ray  series 
of  hydrogen  is  the  ordinary  Balmer  series  in  the  visible 
region,  the  head  of  which  is  at  X=365juju.  In  other 
words,  hydrogen's  ordinary  radiations  are  its  X-rays 
and  nothing  more. 

There  is  also  an  M  series  for  hydrogen  discovered  by 
Paschen  in  the  ultra-red,  which  in  itself  would  make  it 
probable  that  there  are  series  for  all  the  elements  of 
longer  wave-length  than  the  L  series,  and  that  the 
complicated  optical  series  observed  with  metallic  arcs 
are  parts  of  these  longer  wave-length  series.  As  a 
matter  of  fact,  an  M  series  has  been  found  for  six  of  the 
elements  of  high  atomic  number. 

Thus  the  Moseley  experiments  have  gone  a  long 
way  toward  solving  the  mystery  of  spectral  lines. 
They  reveal  to  us  clearly  and  certainly  the  whole  series 
of  elements  from  hydrogen  to  uranium,. all  producing 
spectra  of  remarkable  similarity,  at  least  so  far  as  the  K 
and  L  radiations  are  concerned,  but  scattered  regularly 
through  the  whole  frequency  region,  from  the  ultra- 
violet, where  the  K  lines  for  hydrogen  are  found,  all 
the  way  up  to  frequencies  (92)*  or  8,464  times  as  high. 
There  can  scarcely  be  a  doubt  that  this  whole  field  will 
soon  be  open  to  exploration.  How  brilliantly,  then, 
have  these  recent  studies  justified  the  predictions  of  the 
spectroscopists  that  the  key  to  atomic  structure  lay 
in  the  study  of  spectral  lines! 

Moseley's  work  is,  in  brief,  evidence  from  a  wholly 
new  quarter  that  all  these  elements  constitute  a  family, 
each  member  of  which  is  related  to  every  other  member 
in  a  perfectly  definite  and  simple  way.  It  looks  as  if 


THE  STRUCTURE  OF  THE  ATOM      203 

the  dream  of  Thales  of  Miletus  had  actually  come  true 
and  that  we  have  not  only  found  a  primordial  element 
out  of  which  all  substances  are  made,  but  that  that  prim- 
ordial element  is  hydrogen  itself.  It  is  well  known  that 
this  result  was  suggested  by  Prout  just  one  hundred 
years  ago,  arguing  as  he  did  from  the  fact  that  most  of 
the  atomic  weights  of  all  the  elements  are  very  nearly 
exact  multiples  of  the  weight  of  hydrogen.  Prout's 
theory  failed  of  general  acceptance  because  the  multiple 
relationships  are  not  found  to  be  exact.  These  depart- 
ures from  exactness  in  the  case  of  the  atomic  weights 
must,  of  course,  be  explained  somehow,  but  if  mass  is 
electromagnetic  in  its  origin,  it  is  not  impossible  to 
explain  them  on  the  basis  of  the  overlapping  of  the 
electric  fields  of  the  electronic  constituents  of  the  atoms. 
Thus,  if  a  positive  and  negative  charge  could  be  brought 
into  exact  coincidence,  their  fields  would  entirely  disap- 
pear, and  with  them  their  masses  also,  provided  mass  is 
merely  a  property  of  an  electric  field.  If,  then,  when 
the  positive  nucleus  of  the  hydrogen  atom  enters  into 
the  nucleus  of  a  heavier  atom,  it  is  packed  very  close  to 
negative  electrons,  the  mass  of  that  nucleus  would  be 
somewhat  less  than  the  sum  of  the  masses  of  the  hydro- 
gen atoms  which  it  contains,  as  it  is  found  in  fact  to  be. 
This  explanation  on  the  basis  of  close  "packing"  of  the 
lack  of  exactness  in  the  multiple  relations  between  the 
atomic  weights  of  the  elements  was  suggested  about 
1901,  as  soon  as  the  Kaufmann1  experiments  had  given 
an  experimental  basis  for  the  electromagnetic  theory  of 
the  origin  of  mass.  It  has  been  discussed  by  Lorenz,  by 

1  Kaufmann,  Gottinger  Nachrichten,  November  8,  1901. 


204  THE  ELECTRON 

Rutherford,1  and  later  by  Harkins.2  With  its  aid  we 
can  account  for  the  lack  of  exact  coincidence  between 
the  progression  of  atomic  weights,  and  that  found  in 
Moseley's  table.  (See  Appendix  H.) 

Whether  or  not  hydrogen  is  the  building-stone  of  all 
the  92  elements  of  Moseley's  table,  we  may  at  least  feel 
fairly  sure  that  the  number  of  free  positive  electrons  in 
the  nucleus  of  an  atom  is  exactly  the  number  assigned  to 
that  atom  in  Moseley's  table.  This  is,  in  general,  a 
little  less  than  half  the  atomic  weight,  since  the  highest 
number  in  the  table  is  92,  while  the  atomic  weight  of  the 
corresponding  heaviest  known  element,  uranium,  is 
238.5.  It  is  the  positive  charge  on  this  nucleus  which 
obviously  determines  the  number  of  negative  electrons 
which  are  distributed  around  the  nucleus  in  the  outer 
regions  of  the  atom,  and  there  is  just  now  an  increasing 
weight  of  evidence  that  this  number  determines  the 
chemical  affinity  of  the  atom,  and,  indeed,  all  its  chem- 
ical and  physical  properties  except  its  weight.  It  is  for 
this  reason  that  we  now  think  there  can  be  no  more 
different  kinds  of  elements  between  hydrogen  and  ura- 
nium than  those  which  correspond  to  the  92  numbers  in 
Moseley's  table. 

How  these  free  positive  charges  in  the  nucleus  vary- 
ing from  i  to  92  are  held  together  we  do  not  know.  The 
experimental  evidence  at  present  stops  with  the  fact 
that  a  number  of  free  positive  electrons  equal  to  the 
atomic  number  exist  in  the  nucleus  and  that  a  corre- 
sponding number  of  free  negative  electrons  are  held  in 

1  Rutherford,  Phil.  Mag.,  XXI  (1911),  669. 

2  Harkins,  Phil.  Mag.,  XXX  (1915),  723. 


THE  STRUCTURE  OF  THE  ATOM      205 

equilibrium  in  the  outer  regions  of  the  atom.  We  may 
imagine  that  there  are  some  negative  electrons  also 
inside  the  nucleus,  for  they  seem  to  be  shot  out  from  it 
in  radioactive  changes.  Further,  to  take  the  case  of  the 
lightest  of  the  composite  atoms,  helium,  of  atomic  num- 
ber 2,  since  its  nucleus  has  but  two  free  positive  charges, 
while  its  atomic  weight  is  4,  we  may  imagine  that  its 
nucleus  is  actually  made  up  of  4  positive  electrons  which 
are  held  together  by  2  negative  electrons.  In  like  man- 
ner, from  this  point  of  view,  each  nucleus  would  have  a 
number  of  binding  negative  electrons  equal  to  its  atomic 
number,  and  the  number  of  positive  electrons  bound  by 
them  in  the  nucleus  would  be  twice  the  atomic  number, 
each  negative  binding  two  positives.  This  would  leave, 
as  it  should,  an  equal  number  of  negative  electrons  to  be 
held  in  the  outer  regions  of  each  atom. 

But  plausible  as  this  point  of  view  may  be,  it  is  as 
yet  speculative.  This  much,  however,  is  known  with 
certainty,  namely,  that  inside  all  the  atoms  there  are  a 
definite  number  of  two  fundamental  entities,  namely, 
positive  and  negative  electrons,  which  are  known  not  to 
differ  from  one  another  at  all  in  charge,  but  which  do 
seem  to  differ  both  in  mass  and  in  volume.  The  electron 
then  in  its  two  forms  is,  according  to  the  physicists' 
present  view,  the  building-stone  of  the  sub-atomic  world. 
Someone  has  called  it  the  "ultim-atom"  of  twentieth- 
century  science. 

VI.      THE   BOHR   ATOM 

Thus  far  nothing  has  been  said  as  to  whether  the 
electrons  within  the  atom  are  at  rest  or  in  motion,  or, 
if  they  are  in  motion,  as  to  the  character  of  th  motions. 


206  THE  ELECTRON 

In  the  hydrogen  atom,  however,  which  contains,  accord- 
ing to  the  foregoing  evidence,  but  one  positive  and  one 
negative  electron,  there  is  no  known  way  of  preventing 
the  latter  from  falling  into  the  positive  nucleus  unless 
centrifugal  forces  are  called  upon  to  balance  attractions, 
as  they  do  in  the  case  of  the  earth  and  moon.  Accord- 
ingly it  seems  to  be  necessary  to  assume  that  the  negative 
electron  is  rotating  in  an  orbit  about  the  positive.  But 
such  an  orbit  would  normally  be  accompanied  by  a 
continuous  radiation  of  energy  of  continuously  increasing 
frequency  as  the  electron,  by  virtue  of  its  loss  of  energy, 
approached  closer  and  closer  to  the  nucleus.  Yet 
experiment  reveals  no  such  behavior,  for,  so  far  as  we 
know,  hydrogen  does  not  radiate  at  all  unless  it  is 
ionized,  and,  when  it  does  radiate,  it  gives  rise,  not  to  a 
continuous  spectrum,  as  the  foregoing  picture  would 
demand,  but  rather  to  a  line  spectrum  in  which  the 
frequencies  corresponding  to  the  various  lines  are 
related  to  one  another  in  the  very  significant  way  shown 
in  the  photograph  of  Fig.  24  and  represented  by  the 
so-called  B aimer  equation,  which  has  the  form 


(34) 


In  this  formula  v  represents  frequency,  N  a  constant, 
and  »x,  for  all  the  lines  in  the  visible  region,  has  the 
value  2,  while  n2  takes  for  the  successive  lines  the  values 
3,  4,  5,  6,  etc.  In  the  hydrogen  series  in  the  infra-red 
discovered  by  Paschen1  «t=3  and  n2  takes  the  successive 
values  4,  5,  6,  etc.  It  is  since  the  development  of  the 

1  Paschen,  Annalen  der  Physik,  XXVII  (1908),  565. 


THE  STRUCTURE  OF  THE  ATOM      207 

Bohr  theory  that  Lyman1  discovered  his  hydrogen 
series  in  the  ultra-violet  in  which  «x=  i  and  n2=  2,  3,  4, 
etc.  Since  i  is  the  smallest  whole  number,  this  series 
should  correspond,  as  indicated  heretofore,  to  the 
highest  frequencies  of  which  hydrogen  is  capable,  the 
upper  limit  toward  which  these  frequencies  tend  being 
reached  when  nl=  i  and  n2=  oo,  that  is,  when  v—N. 

Guided  by  all  of  these  facts  except  the  last,  N,  Bohr, 
a  young  mathematical  physicist  of  Copenhagen,  has 
recently  devised2  an  atomic  model  which  has  had  some 
very  remarkable  successes.  This  model  was  originally 
designed  to  cover  only  the  simplest  possible  case  of  one 
single  electron  revolving  around  a  positive  nucleus.  In 
order  to  account  for  the  large  number  of  lines  which  the 
spectrum  of  such  a  system  reveals  (Fig.  24,  taken  by 
Professor  Wright  of  the  Lick  Observatory,  shows  all 
of  the  Balmer  series  given  by  the  spectrum  of  a  nebula 
except  the  longest  wave-length  line  called  Ha,  which  is 
beyond  the  left  edge  of  the  plate),  Bohr's  first  assump- 
tion was  that  the  electron  may  rotate  about  the  nucleus 
in  a  whole  series  of  different  orbits  and  that  each  of  these 
orbits  is  governed  by  the  w^ll-known  Newtonian  law, 
which  when  mathematically  stated  takes  the  form: 

(35) 


in  which  e  is  the  change  of  the  electron,  E  that  of  the 
nucleus,  a  the  radius  of  the  orbit,  n  the  orbital  frequency, 
and  m  the  mass  of  the  electron.  This  is  merely  the 

1  Spectroscopy  of  the  Extreme  Ultraviolet,  p.  78. 
*N.  Bohr,  Phil.  Mag.,  XXVI  (1913),  i  and  476  and  857;  XXIX 
(1915),  332;  XXX  (1915),  394. 


208  THE  ELECTRON 

assumption  that  the  electron  rotates  in  a  circular  orbit 
which  is  governed  by  the  laws  which  are  known,  from 
the  work  on  the  scattering  of  the  alpha  particles,  to 
hold  inside  as  well  as  outside  the  atom.  The  radical 
element  in  it  is  that  it  permits  the  negative  electron  to 
maintain  this  orbit  without  radiating  energy  even  though 
this  appears  to  conflict  with  ordinary  electromagnetic 
theory.  But,  on  the  other  hand,  the  facts  of  magnet- 
ism1 and  of  optics,  in  addition  to  the  successes  of 
the  Bohr  theory  which  are  to  be  detailed,  appear  at 
present  to  lend  experimental  justification  to  such  an 
assumption. 

Bohr's  second  assumption  is  that  radiation  takes 
place  only  when  an  electron  jumps  from  one  to  another 
of  these  orbits.  If  A2  represents  the  energy  of  the 
electron  in  one  orbit  and  Al  that  in  any  other  orbit, 
then  it  is  clear  from  considerations  of  energy  alone  that 
when  the  electron  passes  from  the  one  orbit  to  the  other 
the  amount  of  energy  radiated  must  be  A 2—A^  further, 
this  radiated  energy  obviously  must  have  some  frequency 
v,  and,  in  view  of  the  experimental  work  presented  in 
the  next  chapter,  Bohr  placed  it  proportional  to  p,  and 
wrote: 

to=A,-At (36) 

h  being  the  so-called  Planck  constant  to  be  discussed 
later.  It  is  to  be  emphasized  that  this  assumption  gives 
no  physical  picture  of  the  way  in  which  the  radiation 
takes  place.  It  merely  states  the  energy  relations 
which  must  be  satisfied  when  it  occurs. 

1  Einstein  and  De  Haas,  Verh.  der  deutsch.  phys.  Ges.,  XVII  (1915), 
152;  also  Baraett,  Phys.  Rev.,  VI  (1915),  239. 


THE  STRUCTURE  OF  THE  ATOM      209 

Bohr's  third  assumption  is  that  the  various  possible 
circular  orbits  are  determined  by  assigning  to  each 
orbit  a  kinetic  energy  T  such  that 


(37) 


in  which  r  is  a  whole  number,  n  the  orbital  frequency, 
and  h  is  again  Planck's  constant.  This  value  of  T  is 
assigned  so  as  to  make  the  series  of  frequencies  agree 
with  that  actually  observed,  namely,  that  represented 
by  the  Balmer  series  of  hydrogen. 

It  is  to  be  noticed  that,  if  circular  electronic  orbits 
exist  at  all,  no  one  of  these  assumptions  is  arbitrary. 
Each  of  them  is  merely  the  statement  of  the  existing 
experimental  situation.  It  is  not  surprising,  therefore, 
that  they  predict  the  sequence  of  frequencies  found  in 
the  hydrogen  series.  They  have  been  purposely  made 
to  do  so.  But  they  have  not  been  made  with  any  refer- 
ence whatever  to  the  exact  numerical  values  of  these 
frequencies. 

The  evidence  for  the  soundness  of  the  conception 
of  non-radiating  electronic  orbits  is  to  be  looked  for, 
then,  first,  in  the  success  of  the  constants  involved,  and, 
second,  in  the  physical  significance,  if  any,  which 
attaches  to  the  third  assumption.  If  these  constants 
come  out  right  within  the  limits  of  experimental  error, 
then  the  theory  of  non-radiating  electronic  orbits  has 
been  given  the  most  crucial  imaginable  of  tests,  especially 
if  these  constants  are  accurately  determinable. 

What  are  the  facts?  The  constant  of  the  Balmer 
series  in  hydrogen,  that  is,  the  value  of  N  in  equation 
(34),  is  known  with  the  great  precision  attained  in  all 


210  THE  ELECTRON 

wave-length  determinations  and  is  equal  to  3  .  2poX  io15. 
From  the  Bohr  theory  it  is  given  by  the  simplest 
algebra  (Appendix  G)  as 


...............  (38) 

m 

As  already  indicated,  I  have  recently  redetermined1  e 
with  an  estimated  accuracy  of  one  part  in  1,000  and 
obtained  for  it  the  value  4,774X  io~10.  As  will  be  shown 
in  the  next  chapter,  I  have  also  determined  h  photo- 
electrically2  with  an  error,  in  the  case  of  sodium,  of  no 
more  than  one-half  of  i  per  cent,  the  value  for  sodium 
being  6.56Xio~27.  The  value  found  by  Webster3 
by  a  method  recently  discovered  by  Duane  and  Hunt4 
is  6.53Xio~27.  Taking  the  mean  of  these  two  results, 
viz.  6.545  Xio~27,  as  the  most  probable  value,  we  get 

with  the  aid  of  Bucherer's  value  of  —  (i  .  767  X  io7)  which 

is  probably  correct  to  o.i  per  cent,  #=3.  294X10^, 
which  agrees  within  a  tenth  of  i  per  cent  with  the  observed 
value.  This  agreement  constitutes  most  extraordinary 
justification  of  the  theory  of  non-radiating  electronic 
orbits.  It  demonstrates  that  the  behavior  of  the  nega- 
tive electron  in  the  hydrogen  atom  is  at  least  correctly 
described  by  the  equation  of  a  circular  non-radiating 
orbit.  If  this  equation  can  be  obtained  from  some 
other  physical  condition  than  that  of  an  actual  orbit, 

1  R.  A.  Millikan,  Proc.  Nat.  Acad.,  April,  1917. 
*  R.  A.  Millikan,  Phys.  Rev.,  VII  (1916),  362. 
sPhys.  Rev.,  VII  (1916),  599. 
«  Ibid.,  VI  (1915),  168. 


THE  STRUCTURE  OF  THE  ATOM      211 

it  is  obviously  incumbent  upon  those  who  so  hold  to 
show  what  that  condition  is.  Until  this  is  done,  it  is 
justifiable  to  suppose  that  the  equation  of  an  orbit 
means  an  actual  orbit. 

Again,  the  radii  of  the  stable  orbits  for  hydrogen  are 
easily  found  from  Bohr's  assumptions  to  take  the 
mathematical  form  (Appendix  G) 


(  . 
(39) 


In  other  words,  since  r  is  a  whole  number,  the  radii  of 
these  orbits  bear  the  ratios  i,  4,  9,  16,  25.  If  normal 
hydrogen  is  assumed  to  be  that  in  which  the  electron  is 
in  the  inmost  possible  orbit,  namely,  that  for  which 
T=I,  2a,  the  diameter  of  the  normal  hydrogen  atom, 
comes  out  i.iXio"8.  The  best  determination  for 
the  diameter  of  the  hydrogen  molecule  yields  2 .  2X  io~8, 
in  extraordinarily  close  agreement  with  the  prediction 
from  Bohr's  theory.  Further,  the  fact  that  normal 
hydrogen  does  not  absorb  at  all  the  Balmer  series  lines 
which  it  emits  is  beautifully  explained  by  the  foregoing 
theory,  since,  according  to  it,  normal  hydrogen  has  no 
electrons  in  the  orbits  corresponding  to  the  lines  of  the 
Balmer  series.  Again,  the  fact  that  hydrogen  emits  Us 
characteristic  radiations  only  when  it  is  ionized  favors 
the  theory  that  the  process  of  emission  is  a  process  of 
settling  down  to  a  normal  condition  through  a  series  of 
possible  intermediate  states,  and  is  therefore  in  line 
with  the  view  that  a  change  in  orbit  is  necessary  to  the 
act  of  radiation.  Similarly,  the  fact  that  in  the  stars 
there  are  33  lines  in  the  Balmer  series,  while  in  the 


212  THE  ELECTRON 

laboratory  we  never  get  more  than  12,  is  easily  explicable 
from  the  Bohr  theory,  but  no  other  theory  has  offered 
even  a  suggestion  of  an  explanation. 

Another  triumph  of  the  theory  is  that  the  third 
assumption,  devised  to  fit  a  purely  empirical  situation, 
viz.,  the  observed  relations  between  the  frequencies 
of  the  Balmer  series,  is  found  to  have  a  very  simple 
and  illuminating  physical  meaning.  It  is  that  all  the 
possible  values  of  the  angular  momentum  of  the  electron 
rotating  about  the  positive  nucleus  are  exact  multiples 
of  a  particular  value  of  this  angular  momentum.  Angu- 
lar momentum  then  has  in  the  hydrogen  atom  the 
property  of  atomicity.  Such  relationships  do  not  in 
general  drop  out  of  empirical  formulae.  When  they  do, 
we  usually  see  in  them  real  interpretations  of  the 
formulae — not  merely  coincidences. 

Again,  the  success  of  a  theory  is  often  tested  as  much 
by  its  adaptability  to  the  explanation  of  deviations  from 
the  behavior  predicted  by  its  most  elementary  form 
as  by  the  exactness  of  the  fit  between  calculated  and 
observed  results.  The  theory  of  electronic  orbits  has 
had  remarkable  successes  of  this  sort.  Thus  it  predicts 
the  Moseley  law  (33).  But  this  law,  discovered  after- 
ward, was  found  inexact,  and  it  should  be  inexact  when 
there  is  more  than  one  electron  in  the  atom,  as  is  the 
case  save  for  H  atoms  and  for  such  He  atoms  as  have 
lost  one  negative  charge,  and  that  because  of  the  way 
in  which  the  electrons  influence  one  another's  fields. 
It  will  probably  be  found  to  break  down  completely 
for  very  light  atoms  like  those  of  lithium.  The  more 
powerful  the  nucleus,  however,  and  the  closer  to  it  the 
inner  orbit  the  smaller  should  this  effect  be.  Now 


THE  STRUCTURE  OF  THE  ATOM  213 

precisely  this  result  is  observed.  The  Moseley  law 
holds  most  accurately  when  tested  for  hydrogen  and 
the  elements  of  highest  atomic  number,  and  much  less 
accurately  when  tested  for  hydrogen  and  aluminum  or 
magnesium.  Similarly  the  ratio  between  the  frequencies 
of  the  a  and  /3  lines  of  the  K  series  approaches  closer 
to  the  theoretical  value  (that  for  hydrogen)  the  higher 
the  atomic  number  of  the  element. 

Again,  it  is  shown  in  the  photographs  opposite  p.  195 
that  the  various  lines  in  the  characteristic  X-ray  spectra 
are  not  single  lines  as  required  by  the  simple  theory. 
Accordingly  Sommerfeld1  extended  Bohr  equations  in 
the  endeavor  to  account  for  this  structure  on  the  basis 
of  ellipticity  in  some  of  the  orbits,  and  Paschen,2  by 
measurements  on  the  structure  of  the  complex  helium 
'lines,  has  obtained  such  extraordinary  checks  upon  this 

theory  that  -'-  comes  out  from  his  measurements  to 
m 

within  a  tenth  of  i  per  cent  of  the  accepted  value. 

A  further  prediction  made  by  the  theory  and  dis- 
covered as  soon  as  looked  for  was  a  relation  between  the 
frequencies  of  the  lines  of  two  succeeding  series  like 
the  K  and  the  L  series.  This  relation  is  expressed  in 
the  equation: 

VRJ3  —  "Ka  =VLa.  . (4°) 

Thus,  according  to  Bohr,  the  longest  wave-length  line 
of  the  K  series,  the  a  line,  is  due  to  jumping  from  orbit  2 
(Fig.  26)  to  orbit  i  with  a  change  in  energy  A^—A^ 
the  next  longest  wave-length  line,  the  /3  line  is  due  to 

1  Annalen  der  Physik,  LI  (1916),  i. 

2  Ibid.,  October,  1916. 


214 


THE  ELECTRON 


jumping  from  3  to  i  with  a  change  in  energy  A^—At', 
while  the  longest  wave-length  line  of  the  L  series,  the 
a  line,  is  due  to  jumping  from  3  to  2,  with  a  change 
in  energy  A  3— A  2.  Hence  if  the  frequency  v  is  in  every 
case  proportional  to  the  change  in  energy,  equation  (40) 
follows  at  once,  and,  further,  it  should  hold  accurately 
from  the  energy  relations  between  the  orbits  whether 
there  be  one  or  many  electrons  in  the  atoms.  I  have  been 

able  to  find  no  case  of  its 
failure,  though  the  data 
upon  which  it  may  be 
tested  are  now  consider- 
able. I  have  also  recently 
pointed  out1  that  it  is 
equivalent  to  the  well- 
known  Rydberg-Schuster 
law,2  which  has  been 
found  to  hold  quite 
generally  among  optical 
series. 

If  then  the  test  of  truth  in  a  physical  theory  is  large 
success  both  in  the  prediction  of  new  relationships  and 
in  correctly  and  exactly  accounting  for  old  ones,  the 
theory  of  non-radiating  orbits,  is  one  of  the  well- 
established  truths  of  modern  physics.  For  the  present  at 
least  it  is  truth,  and  no  other  theory  of  atomic  structure 
need  be  considered  until  it  has  shown  itself  able  to 
approach  it  in  fertility.  I  know  of  no  competitor  which 
is  as  yet  even  in  sight. 

IPhys.  Rev.,  May,  1917,  presented  before  the  American  Physical 
Society,  December  i,  1916. 

2  Baly's  Spectroscopy,  p.  488. 


FIG.  26 


THE  STRUCTURE  OF  THE  ATOM      215 

I  am  well  aware  that  the  facts  of  organic  chemistry 
seem  to  demand  that  the  valence  electrons  be  grouped 
in  certain  definite  equilibrium  positions  about  the 
periphery  of  the  atom,  and  that  at  first  sight  this  demand 
appears  difficult  to  reconcile  with  the  theory  of  electronic 
orbits.  As  yet,  however,  there  is  no  necessary  clash. 
Hydrogen  and  helium  present  no  difficulties,  since  the 
former  has  but  one  valency,  and  the  latter  none.  It 
is  to  these  atoms  alone  that  the  unmodified  Bohr  theory 
applies,  for  it  treats  only  the  case  of  a  single  negative 
electron  rotating  about  a  positive  nucleus.  That  the 
K  radiations  of  the  heavy  elements  are  so  accurately 
predictable  from  those  of  hydrogen  indicates,  indeed, 
that  close  to  the  nucleus  of  these  elements  there  lie 
electrons  to  which  the  Bohr  theory  applies  fairly  accur- 
ately, but  the  radiations  give  us  no  information  about 
the  conditions  or  behaviors  of  the  external  electrons 
which  have  to  do  with  the  phenomena  of  valency,  and 
we  have  investigated  but  little  the  radiating  properties  of 
the  atoms  which  possess  but  few  electrons.  A  further 
study  of  the  behavior  with  respect  to  X-rays  of  the 
elements  from  lithium,  atomic  number  3,  to  magnesium, 
atomic  number  n,  may  be  expected  to  throw  new  light 
on  this  problem. 

It  has  been  objected,  too,  that  the  Bohr  theory  is 
not  a  radiation  theory  because  it  gives  us  no  picture 
of  the  mechanism  of  the  production  of  the  frequency  v. 
This  is  true,  and  therein  lies  its  strength,  just  as  the 
strength  of  the  first  and  second  laws  of  thermodynamics 
lies  in  the  fact  that  they  are  true  irrespective  of  a  mechan- 
ism. The  Bohr  theory  is  a  theory  of  atomic  structure; 
it  is  not  a  theory  of  radiation,  for  it  merely  states  what 


216  THE  ELECTRON 

energy  relations  must  exist  when  radiation,  whatever 
its  mechanism,  takes  place.  It  is  the  first  attempt  to 
determine  in  the  light  of  well-established  experimental 
facts  what  the  electrons  inside  the  atom  are  doing,  and 
as  such  a  first  attempt  it  must  be  regarded  as,  thus  far, 
a  success,  though  it  has  by  no  means  got  beyond  the 
hypothetical  stage.  Its  chief  difficulty  arises  from  the 
apparent  contradiction  involved  in  a  non-radiating 
electronic  orbit — a  contradiction  which  would  disappear, 
however,  if  the  negative  electron  itself,  when  inside  the 
atom,  were  a  ring  of  some  sort,  capable  of  expanding  to 
various  radii,  and  capable,  only  when  freed  from  the 
atom,  of  assuming  essentially  the  properties  of  a  point 
charge,  such  as  we  find  it  endowed  with  in  experiments 
upon  cathode  rays,  j8-rays,  and  ionization  in  gases. 
That  it  actually  does  possess  certain  properties  not  in 
the  past  always  associated  with  electrical  charges  will 
appear  in  the  next  chapter. 


CHAPTER  X 
THE  NATURE  OF  RADIANT  ENERGY 

The  problems  thus  far  discussed  have  all  been  in  the 
domain  of  molecular  physics,  but  the  discovery  and 
measurement  of  the  electron  have  also  exerted  a  powerful 
influence  upon  recent  developments  in  the  domain  of 
ether  physics.  These  developments  are  of  extraordinary 
interest  and  suggestiveness,  but  they  lead  into  regions  in 
which  the  physicist  sees  as  yet  but  dimly — indeed  even 
more  dimly  than  he  thoilght  he  saw  twenty  years  ago. 

But  while  the  beauty  of  a  problem  solved  excites  the 
admiration  and  yields  a  certain  sort  of  satisfaction,  it  is 
after  all  the  unsolved  problem,  the  quest  of  the  unknown, 
the  struggle  for  the  unattained,  which  is  of  most  universal 
and  most  thrilling  interest.  I  make  no  apologies,  there- 
fore, for  introducing  in  this  chapter  one  of  the  great 
unsolved  problems  of  modern  physics,  nor  for  leaving  it 
with  but  the  vaguest  of  suggestions  toward  a  solution. 

I.      THE  CORPUSCULAR  AND   THE  ETHER   THEORIES   OF 
RADIATION 

The  newest  of  the  problems  of  physics  is  at  the  same 
time  the  oldest.  For  nothing  is  earlier  in  the  experiences 
either  of  the  child  or  of  the  race  than  the  sensation  of 
receiving  light  and  heat  from  the  sun.  But  how  does  light 
get  to  us  from  the  sun  and  the  stars  through  the  empty 
interstellar  spaces  ?  The  Greeks  answered  this  query 
very  simply  and  very  satisfactorily  from  the  standpoint 
of  people  who  were  content  with  plausible  explanations 

217 


218  THE  ELECTRON 

but  had  not  yet  learned  perpetually  to  question  nature 
experimentally  as  to  the  validity  or  invalidity  of  a 
conclusion.  They  said  that  the  sun  and  all  radiators 
of  light  and  heat  must  shoot  off  minute  corpuscles  whose 
impact  upon  the  eye  or  skin  produces  the  sensations 
of  light  and  warmth. 

This  corpuscular  theory  was  the  generally  accepted 
one  up  to  1800  A.D.  It  was  challenged,  it  is  true,  about 
1680  by  the  Dutch  physicist  Huygens,  who,  starting  with 
the  observed  phenomena  of  the  transmission  of  water 
waves  over  the  surface  of  a  pond  or  of  sound  waves 
through  the  air,  argued  that  light  might  be  some  vibra- 
tory disturbance  transmitted  by  some  medium  which  fills 
all  interstellar  space.  He  postulated  the  existence  of 
such  a  medium,  which  was  called  the  luminiferous  or 
light-bearing  ether. 

Partly  no  doubt  because  of  Newton's  espousal  of  the 
corpuscular  theory,  the  ether  or  wave  theory  gained  few 
adherents  until  some  facts  of  interference  began  to  appear 
about  1800  which  baffled  explanation  from  the  stand- 
point of  the  corpuscular  theory,  but  which  were  easily 
handled  by  its  rival.  During  the  nineteenth  century  the 
evidence  became  stronger  and  stronger,  until  by  its  close 
the  corpuscular  theory  had  been  permanently  eliminated 
for  four  different  reasons:  (i)  The  facts  of  interference 
were  not  only  found  inexplicable  in  terms  of  it,  but  they 
were  completely  predicted  by  the  wave  theory.  (2)  The 
fact  that  the  speed  of  propagation  of  light  was  experi- 
mentally found  to  be  greater  in  air  than  in  water  was  in 
accord  with  the  demands  of  the  ether  theory,  but  directly 
contrary  to  the  demands  of  the  corpuscular  theory. 
(3)  Wireless  waves  had  appeared  and  had  been  shown 


THE  NATURE  OF  RADIANT  ENERGY     219 

to  be  just  like  light  waves  save  for  wave-length,  and  they 
had  been  found  to  pass  over  continuously,  with  increas- 
ing wave-length,  into  static  electrical  fields  such  as  could, 
not  possibly  be  explained  from  a  corpuscular  point  of 
view.  (4)  The  speed  of  light  had  been  shown  to  be  inde- 
pendent of  the  speed  of  the  source  as  demanded  by  the 
ether  theory  and  denied  by  the  corpuscular  theory. 

By  1900,  then,  the  ether  theory  had  become  apparently 
impregnably  intrenched.  A  couple  of  years  later  it  met 
with  some  opposition  of  a  rather  ill-considered  sort,  as 
it  seems  to  me,  from  a  group  of  extreme  advocates  of  the 
relativity  theory,  but  this  theory  is  now  commonly 
regarded,  I  think,  as  having  no  bearing  whatever  upon 
the  question  of  the  existence  or  non-existence  of  a  lumi- 
niferous  ether.  For  such  an  ether  was  called  into  being 
solely  for  the  sake  of  furnishing  a  carrier  for  electro- 
magnetic waves,  and  it  obviously  stands  or  falls  with  the 
existence  of  such  waves  in  vacuo,  and  this  has  never  been 
questioned  by  anyone  so  far  as  I  am  aware. 

II.      DIFFICULTIES  CONFRONTING  THE  WAVE  THEORY 

Up  to  1903,  then,  the  theory  which  looked  upon  an 
electromagnetic  wave  as  a  disturbance  which  originated 
at  some  point  in  the  ether  at  which  an  electric  charge  was 
undergoing  a  change  in  speed,  and  was  propagated  from 
that  point  outward  as  a  spherical  wave  or  pulse,  the  total 
energy  of  the 'disturbance  being  always  spread  uniformly 
over  the  wave  front,  had  met  with  no  serious  question 
from  any  source.  Indeed,  it  had  been  extraordinarily 
successful,  not  only  in  accounting  for  all  the  known  facts, 
but  in  more  than  one  instance  in  predicting  new  ones. 
The  first  difficulty  appeared  after  the  discovery  of  the 


220  THE  ELECTRON 

electron  and  in  connection  with  the  relations  of  the  elec- 
tron to  the  absorption  or  emission  of  such  electro- 
magnetic waves.  It  was  first  pointed  out  in  1903  by 
Sir  J.  J.  Thomson  in  his  Silliman  lectures  at  Yale.  It 
may  be  stated  thus: 

X-rays  unquestionably  pass  over  or  pass  all  but  an 
exceedingly  minute  fraction,  say  one  in  a  thousand 
billion,  of  the  atoms  contained  in  the  space  traversed 
without  spending  any  energy  upon  them  or  influencing 
them  in  any  observable  way.  But  here  and  there  they 
find  an  atom  from  which,  as  is  shown  in  the  photographs 
opposite  p.  189,  they  hurl  a  negative  electron  with  enor- 
mous speed.  This  is  the  most  interesting  and  most 
significant  characteristic  of  X-rays,  and  one  which  dis- 
tinguishes them  from  the  a-  and  /3-rays  just  as  sharply 
as  does  the  property  of  non-deviability  in  a  magnetic 
field;  for  Figs.  14  and  15  and  the  plate  opposite  p.  189 
show  that  neither  a-  nor  /3-rays  ever  eject  electrons  from 
the  atoms  through  which  they  pass,  with  speeds  com- 
parable with  those  produced  by  X-rays,  else  there  would 
be  new  zigzag  lines  branching  out  from  points  all  along 
the  paths  of  the  a-  and  /3-particles  shown  in  these  photo- 
graphs. 

But  this  property  of  X-rays  introduces  a  serious 
difficulty  into  the  ether  theory.  For  if  the  electric 
intensity  in  the  wave  front  of  the  X-ray  is  sufficient  thus 
to  hurl  a  corpuscle  with  huge  energy  from  one  particular 
atom,  why  does  it  not  at  least  detach  corpuscles  from 
all  of  the  atoms  over  which  it  passes  ? 

Again  when  ultra-violet  light  falls  on  a  metal  it,  too, 
like  X-rays,  is  found  to  eject  negative  electrons.  This 
phenomenon  of  the  emission  of  corpuscles  under  the 


THE  NATURE  OF  RADIANT  ENERGY     221 

influence  of  light  is  called  the  photo-electric  effect. 
Lenard1  first  made  the  astonishing  discovery  that  the 
energy  of  ejection  of  the  corpuscle  is  altogether  independ- 
ent of  the  intensity  of  the  light  which  causes  the  ejection, 
no  matter  whether  this  intensity  is  varied  by  varying 
the  distance  of  the  light  or  by  introducing  absorbing 
screens.  I  have  myself2  subjected  this  relation  to  a  very 
precise  test  and  found  it  to  hold  accurately.  Further- 
more, this  sort  of  independence  has  also  been  established 
for  the  negative  electrons  emitted  by  both  X-  and7-rays. 

Facts  of  this  sort  are  evidently  difficult  to  account  for 
on  any  sort  of  a  spreading- wave  theory.  But  it  will  be 
seen  that  they  lend  themselves  to  easy  interpretation  in 
terms  of  a  corpuscular  theory,  for  if  the  energy  of  an 
escaping  electron  comes  from  the  absorption  of  a  light- 
corpuscle,  then  the  energy  of  emission  of  the  ejected 
electron  ought  to  be  independent  of  the  distance  of  the 
source,  as  it  is  found  to  be,  and  furthermore  corpuscular 
rays  would  hit  but  a  very  minute  fraction  of  the  atoms 
contained  in  the  space  traversed  by  them.  This  would 
explain,  then,  both  the  independence  of  the  energy  of 
emission  upon  intensity  and  the  smallness  of  the  number 
of  atoms  ionized. 

In  view,  however,  of  the  four  sets  of  facts  mentioned 
above,  Thomson  found  it  altogether  impossible  to  go 
back  to  the  old  and  exploded  form  of  corpuscular  theory 
for  an  explanation  of  the  new  facts  as  to  the  emission  of 
electrons  under  the  influence  of  ether  waves.  He 
accordingly  attempted  to  reconcile  these  troublesome 
new  facts  with  the  wave  theory  by  assuming  a  fibrous 

1  Ann.  d.  Phys.  (4),  VIII  (1902),  149. 
2Phys.  Rev.,  I  (1913),  73- 


222  THE  ELECTRON 

structure  in  the  ether  and  picturing  all  electromagnetic 
energy  as  traveling  along  Faraday  lines  of  force  con- 
ceived of  as  actual  strings  extending  through  all  space. 
Although  this  concept,  which  we  shall  call  the  ether- 
string  theory,  is  like  the  corpuscular  theory  in  that  the 
energy,  after  it  leaves  the  emitting  body,  remains  local- 
ized in  space,  and,  when  absorbed,  is  absorbed  as  a  whole, 
yet  it  is  after  all  essentially  an  ether  theory.  For  in  it 
the  speed  of  propagation  is  determined  by  the  properties 
of  the  medium  and  has  nothing  to  do  with  the  nature  or 
condition  of  the  source.  Thus  the  last  three  of  the  fatal 
objections  to  a  corpuscular  theory  are  not  here  encoun- 
tered. As  to  the  first  one,  no  one  has  yet  shown  that 
Thomson's  suggestion  is  reconcilable  with  the  facts  of 
interference,  though  so  far  as  I  know  neither  has  its 
irreconcilability  been  as  yet  absolutely  demonstrated. 

But  interference  aside,  all  is  not  simple  and  easy  for 
Thomson's  theory.  For  one  encounters  serious  diffi- 
culties when  he  attempts  to  visualize  the  universe  as  an 
infinite  cobweb  whose  threads  never  become  tangled  or 
broken  however  swiftly  the  electrical  charges  to  which 
they  are  attached  may  be  flying  about. 

in.    EINSTEIN'S  QUANTUM  THEORY  or  RADIATION 

Yet  the  boldness  and  the  difficulties  of  Thomson's 
"ether-string"  theory  did  not  deter  Einstein1  in  1905 
from  making  it  even  more  radical.  In  order  to  connect 
it  up  with  some  results  to  which  Planck  of  Berlin  had 
been  led  in  studying  the  facts  of  black-body  radiation, 
Einstein  assumed  that  the  energy  emitted  by  any  radiator 
not  only  kept  together  in  bunches  or  quanta  as  it  traveled 
.  d.  Phys.  (4),  XVII  (1905),  132;  XX  (1906),  199. 


THE  NATURE.  OF  RADIANT  ENERGY  223 

through  space,  as  Thomson  had  assumed  it  to  do,  but 
that  a  given  source  could  emit  and  absorb  radiant  energy 
only  in  units  which  are  all  exactly  equal  to  hv,  v  being 
the  natural  frequency  of  the  emitter  and  h  a  constant 
which  is  the  same  for  all  emitters. 

I  shall  not  attempt  to  present  the  basis  for  such  an 
assumption,  for,  as  a  matter  of  fact,  it  had  almost  none 
at  the  time.  But  whatever  its  basis,  it  enabled  Einstein 
to  predict  at  once  that  the  energy  of  emission  of  cor- 
puscles under  the  influence  of  light  would  be  governed 
by  the  equation 

Ve  =  hv—  p  ...............  (41) 


in  which  hv  is  the  energy  absorbed  by  the  electron  from 
the  light  wave  or  light  quantum,  for,  according  to  the 
assumption  it  was  the  whole  energy  contained  in  that 
quantum,  p  is  the  work  necessary  to  get  the  electron 
out  of  the  metal,  and  %mv2  is  the  energy  with  which  it 
leaves  the  surface  —  an  energy  evidently  measured  -by  the 
product  of  its  charge  e  by  the  potential  difference  V 
against  which  it  is  just  able  to  drive  itself  before  being 
brought  to  rest. 

At  the  time  at  which  it  was  made  this  prediction  was 
as  bold  as  the  hypothesis  which  suggested  it,  for  at  that 
time  there  were  available  no  experiments  whatever  for 
determining  anything  about  how  the  positive  potential 
V  necessary  to  apply  to  the  illuminated  electrode  to  stop 
the  discharge  of  negative  electrons  from  it  under  the 
influence  of  monochromatic  light  varied  with  the  fre- 
quency v  of  the  light,  or  whether  the  quantity  h  to  which 
Planck  had  already  assigned  a  numerical  value  appeared 
at  all  in  connection  with  photo-electric  discharge.  We 


224  THE  ELECTRON 

are  confronted,  however,  by  the  astonishing  situation 
that  after  ten  years  of  work  at  the  Ryerson  Laboratory 
and  elsewhere  upon  the  discharge  of  electrons  by  light 
this  equation  of  Einstein's  seems  to  us  to  predict  accu- 
rately all  of  the  facts  which  have  been  observed. 

IV.     THE  TESTING  OF  EINSTEIN'S   EQUATION 

The  method  which  has  been  adopted  in  the  Ryerson 
Laboratory  for  testing  the  correctness  of  Einstein's 
equation  has  involved  the  performance  of  so  many  opera- 
tions upon  the  highly  inflammable  alkali  metals  in  a 
vessel  which  was  freed  from  the  presence  of  all  gases  that 
it  is  not  inappropriate  to  describe  the  present  experi- 
mental arrangement  as  a  machine-shop  in  vacuo.  Fig.  27 
shows  a  photograph  of  the  apparatus,  and  Fig.  28  is  a 
drawing  of  a  section  which  should  make  the  necessary 
operations  intelligible. 

One  of  the  most  vital  assertions  made  in  Einstein's 
theory-  is  that  the  kinetic  energy  with  which  mono- 
chromatic light  ejects  electrons  from  any  metal  is 
proportional  to  the  frequency  of  the  light,  i.e.,  if  violet 
light  is  of  half  the  wave-length  of  red  light,  then  the 
violet  light  should  throw  out  the  electron  with  twice 
the  energy  imparted  to  it  by  the  red  light.  In  order  to 
test  whether  any  such  linear  relation  exists  between  the 
energy  of  the  escaping  electron  and  the  light  which 
throws  it  out  it  was  necessary  to  use  as  wide  a  range  of 
frequencies  as  possible.  This  made  it  necessary  to  use 
the  alkali  metals,  sodium,  potassium,  and  lithium,  for 
electrons  are  thrown  from  the  ordinary  metals  only  by 
ultra-violet  light,  while  the  alkali  metals  respond  in  this 
way  to  any  waves  shorter  than  those  of  the  red,  that  is, 


THE  NATURE  OF  RADIANT  ENERGY 


225 


they  respond  throughout  practically  the  whole  visible 
spectrum  as  well  as  the  ultra-violet  spectrum.  Cast 
cylinders  of  these  metals  were  therefore  placed  on  the 
wheel  W  (Fig.  28)  and  fresh  clean  surfaces  were  obtained 
by  cutting  shavings  from  each  metal  in  an  excellent 
vacuum  with  the  aid  of  the  knife  K,  which  was  operated 


FIG.  27 

by  an  electromagnet  F  outside  the  tube.  After  this  the 
freshly  cut  surface  was  turned  around  by  another  electro- 
magnet until  it  was  opposite  the  point  O  of  Fig..  28  and 
a  beam  of  monochromatic  light  from  a  spectrometer  was 
let  in  through  0  and  allowed  to  fall  on  the  new  surface. 
The  energy  of  the  electrons  ejected  by  it  was  measured 
by  applying  to  the  surface  a  positive  potential  just  strong 
enough  to  prevent  any  of  the  discharged  electrons  from 


226 


THE  ELECTRON 


reaching  the  gauze  cylinder  opposite  (shown  in  dotted 
lines)  and  thus  communicating  an  observable  negative 


charge  to  the  quadrant  electrometer  which  was  attached 
to  this  gauze  cylinder.    For  a  complete  test  of  the 


THE  NATURE  OF  RADIANT  ENERGY     227 

equation  it  was  necessary  also  to  measure  the  contact- 
electromotive  force  between  the  new  surface  and  a  test 
plate  S.  This  was  done  by  another  electromagnetic 
device  shown  in  Fig.  27,  but  for  further  details  the  original 
paper  may  be  consulted.1  Suffice  it  here  to  say  that 
Einstein's  equation  demands  a  linear  relation  between 
the  applied  positive  volts  and  the  frequency  of  the  light, 
and  it  also  demands  that  the  slope  of  this  line  should  be 

exactly  equal  to  -  .     Hence  from  this  slope,  since  e  is 

known,  it  should  be  possible  to  obtain  h.  How  per- 
fect a  linear  relation  is  found  may  be  seen  from  Fig.  29, 
which  also  shows  that  from  the  slope  of  this  line  h  is 
found  to  be  6.  26Xio~27,  which  is  as  close  to  the  value 
obtained  by  Planck  from  the  radiation  laws  as  is  to 
be  expected  from  the  accuracy  with  which  the  experi- 
ments in  radiation  can  be  made.  The  most  reliable 
value  of  h  obtained  from  a  consideration  of  the  whole  of 
this  work  is 


In  the  original  paper  will  be  found  other  tests  of  the 
Einstein  equation,  but  the  net  result  of  all  this  work  is  to 
confirm  in  a  very  complete  way  the  equation  which 
Einstein  first  set  up  on  the  basis  of  his  semi-corpuscular 
theory  of  radiant  energy.  And  if  this  equation  is  of 
general  validity  it  must  certainly  be  regarded  as  one  of 
the  most  fundamental  and  far-reaching  of  the  equations 
of  physics,  and  one  which  is  destined  to  play  in  the  future 
a  scarcely  less  important  role  than  Maxwell's  equations 
have  played  in  the  past,  for  it  must  govern  the  trans- 
1  Phys.  Rev.,  VII  (1916),  363, 


THE  NATURE  OF  RADIANT  ENERGY     229 

formation    of    all    short-wave-length    electromagnetic 
energy  into  heat  energy. 

V.     OBJECTIONS  TO  AN  ETHER-STRING  THEORY 

In  spite  of  the  credentials  which  have  just  been  pre- 
sented for  Einstein's  equation,  we  are  confronted  with 
the  extraordinary  situation  that"  the  semi-corpuscular 
theory  out  of  which  Einstein  got  his  equation  seems  to 
be  wholly  untenable  and  has  in  fact  been  pretty  gener- 
ally abandoned,  though  Sir  J.  J.  Thomson1  and  a  few 
others2  seem  still  to  adhere  to  some  form  of  ether- 
string  theory,  that  is,  to  some  form  of  theory  in  which 
the  energy  remains  localized  in  space  instead  of  spreading 
over  the  entire  wave  front. 

Two  very  potent  objections,  however,  may  be  urged 
against  all  forms  of  ether-string  theory,  of  which 
Einstein's  is  a  particular  modification.  The  first  is 
that  no  one  has  ever  yet  been  able  to  show  that 
such  a  theory  can  predict  any  one  of  the  facts  of  inter- 
ference. The  second  is  that  there  is  direct  positive  evi- 
dence against  the  view  that  the  ether  possesses  a  fibrous 
structure.  For  if  a  static  electrical  field  has  a  fibrous 
structure,  as  postulated  by  any  form  of  ether-string 
theory,  "each  unit  of  positive  electricity  being  the  origin 
and  each  unit  of  negative  electricity  the  termination  of 
a  Faraday  tube,"3  then  the  force  acting  on  one  single 
electron  between  the  plates  of  an  air  condenser  cannot 
possibly  vary  continuously  with  the  potential  difference 

1  Proc.  Phys.  Soc.  of  London,  XXVII  (December  15,  1914),  105. 
3  Modern  Electrical  Theory,  Cambridge,  University  Press,    1913, 
p.  248. 

3  J.  J.  Thomson,  Electricity  and  Matter,  p.  9. 


230  THE  ELECTRON 

between  the  plates.  Now  in  the  oil-drop  experiments1 
we  actually  study  the  behavior  in  such  an  electric  field 
of  one  single,  isolated  electron  and  we  find,  over  the 
widest  limits,  exact  proportionality  between  the  field 
strength  and  the  force  acting  on  the  electron  as  measured 
by  the  velocity  with  which  the  oil  drop  to  which  it  is 
attached  is  dragged  through  the  air. 

When  we  maintain  the  field  constant  and  vary  the 
charge  on  the  drop,  the  granular  structure  of  electricity  is 
proved  by  the  discontinuous  changes  in  the  velocity,  but 
when  we  maintain  the  charge  constant  and  vary  the  field 
the  lack  of  discontinuous  change  in  the  velocity  disproves 
the  contention  of  a  fibrous  structure  in  the  field,  unless  the 
assumption  be  made  that  there  are  an  enormous  number 
of  ether  strings  ending  in  one  electron.  Such  an  assump- 
tion takes  all  the  virtue  out  of  an  ether-string  theory. 

Despite  then  the  apparently  complete  success  of  the 
Einstein  equation,  the  physical  theory  of  which  it  was 
designed  to  be  the  symbolic  expression  is  found  so 
untenable  that  Einstein  himself,  I  believe,  no  longer 
holds  to  it,  and  we  are  in  the  position  of  having  built  a 
very  perfect  structure  and  then  knocked  out  entirely 
the  underpinning  without  causing  the  building  to  fall. 
It  stands  complete  and  apparently  well  tested,  but  with- 
out any  visible  means  of  support.  These  supports  must 
obviously  exist,  and  the  most  fascinating  problem  of 
modern  physics  is  to  find  them.  Experiment  has  outrun 
theory,  or,  better,  guided  by  erroneous  theory,  it  has 
discovered  relationships  which  seem  to  be  of  the  greatest 
interest  and  importance,  but  the  reasons  for  them  are  as 
yet  not  at  all  understood. 

1  Phys.  Rev.,  II  (1913),  109, 


THE  NATURE  OF  RADIANT  ENERGY  231 

VI.      ATTEMPTS   TOWARD  A   SOLUTION 

It  is  possible,  however,  to  go  a  certain  distance 
toward  a  solution  and  to  indicate  some  conditions  which 
must  be  satisfied  by  the  solution  when  it  is  found.  For 
the  energy  hv  with  which  the  electron  is  found  by  experi- 
ment to  escape  from  the  atom  must  have  come  either 
from  the  energy  stored  up  inside  of  the  atom  or  else  from 
the  light.  There  is  no  third  possibility.  Now  the  fact 
that  the  energy  of  emission  is  the  same,  whether  the  body 
from  which  it  is  emitted  is  held  within  an  inch  of  the 
source,  where  the  light  is  very  intense,  or  a  mile  away, 
where  it  is  very  weak,  would  seem  to  indicate  that  the 
light  simply  pulls  a  trigger  in  the  atom  which  itself  fur- 
nishes all  the  energy  with  which  the  electron  escapes,  as 
was  originally  suggested  by  Lenard  in  1902,*  or  else,  if 
the  light  furnishes  the  energy,  that  light  itself  must 
consist  of  bundles  of  energy  which  keep  together  as  they 
travel  through  space,  as  suggested  in  the  Thomson- 
Einstein  theory. 

Yet  the  fact  that  the  energy  of  emission  is  directly 
proportional  to  the  frequency  v  of  the  incident  light 
spoils  Lenard's  form  of  trigger  theory,  since,  if  the  atom 
furnishes  the  energy,  it  ought  to  make  no  difference  what 
kind  of  a  wave-length  pulls  the  trigger,  while  it  ought  to 
make  a  difference  what  kind  of  a  gun,  that  is,  what  kind 
of  an  atom,  is  shot  off.  But  both  of  these  expectations 
are  the  exact  opposite  of  the  observed  facts.  The  energy 
of  the  escaping  corpuscle  must  come  then,  in  some  way  or 
other,  from  the  incident  light. 

When,  however,  we  attempt  to  compute  on  the  basis 
of  a  spreading- wave  theory  how  much  energy  a  corpuscle 

1  Ann.  d.  Phys.  (4),  VIII  (1902),  149. 


232  THE  ELECTRON 

can  receive  from  a  given  source  of  light,  we  find  it  diffi- 
cult to  find  anything  more  than  a  very  minute  fraction 
of  the  amount  which  the  corpuscle  actually  acquires. 

Thus,  the  total  luminous  energy  falling  per  second 
from  a  standard  candle  on  a  square  centimeter  at  a  dis- 
tance of  3  m.  is  i  erg.1  Hence  the  amount  falling  per 
second  on  a  body  of  the  size  of  an  atom,  i.e.,  of  cross- 
section  io~IS  cm.,  is  io~IS  ergs,  but  the  energy  hv  with 
which  a  corpuscle  is  ejected  by  light  of  wave-length  500  juju 
(millionths  millimeter)  is  4X  io~12  ergs,  or  4,000  times  as 
much.  Since  not  a  third  of  the  incident  energy  is  in 
wave-lengths  shorter  than  500  juju,  a  surface  of  sodium 
or  lithium  which  is  sensitive  up  to  500  W  should  require, 
even  if  all  this  energy  were  in  one  wave-length,  which  it 
is  not,  at  least  12,000  seconds  or  4  hours  of  illumination 
by  a  candle  3  m.  away  before  any  of  its  atoms  could  have 
received,  all  told,  enough  energy  to  discharge  a  corpuscle. 
Yet  the  corpuscle  is  observed  to  shoot  out  the  instant  the 
light  is  turned  on.  It  is  true  that  Lord  Rayleigh  has 
recently  shown2  that  an  atom  may  conceivably  absorb 
wave-energy  from  a  region  of  the  order  of  magnitude  of 
the  square  of  a  wave-length  of  the  incident  light  rather 
than  of  the  order  of  its  own  cross-section.  This  in  no 
way  weakens,  however,  the  cogency  of  the  type  of  argu- 
ment just  presented,  for  it  is  only  necessary  to  apply 
the  same  sort  of  analysis  to  the  case  of  7- rays,  the  wave- 
length of  which  is  of  the  order  of  magnitude  of  an 
atomic  diameter  (io~8cm.);  and  the  difficulty  is  found 
still  more  pronounced.  Thus  Rutherford3  estimates  that 

1  Drude,  Lehrbuch  der  Optik,  1906,  p.  472. 

2  Phil.  Mag.,  XXXII  (1916),  188. 

3  Radioactive  Substances  and  the  Radiations,  p.  288. 


THE  NATURE  OF  RADIANT  ENERGY     233 

the  total  7-ray  energy  radiated  per  second  by  one  gram 
of  radium  cannot  possibly  be  more  than  4.7Xio4  ergs. 
Hence  at  a  distance  of  100  meters,  where  the  7-rays 
from  a  gram  of  radium  would  be  easily  detectable,  the 
total  7- ray  energy  falling  per  second  on  a  square  milli- 
meter of  surface,  the  area  of  which  is  ten- thousand 
billion  times  greater  than  that  either  of  an  atom  or  of  a 
disk  whose  radius  is  a  wave-length,  would  be  4.  yX  io4-r- 
47rX  ioIO=4X  io~7  ergs.  This  is  very  close  to  the  energy 
with  which  /3-rays  are  actually  observed  to  be  ejected 
by  these  7- rays,  the  velocity  of  ejection  being  about 
nine- tenths  that  of  light.  Although,  then,  it  should  take 
ten  thousand  billion  seconds  for  the  atom  to  gather  in 
this  much  energy  from  the  7-rays,  on  the  basis  of  classi- 
cal theory,  the  /5-ray  is  observed  to  be  ejected  with  this 
energy  as  soon  as  the  radium  is  put  in  place.  This 
shows  that  if  we  are  going  to  abandon  the  Thomson- 
Einstein  hypothesis  of  localized  energy,  which  is  of 
course  competent  to  satisfy  these  energy  relations,  there 
is  no  alternative  but  to  assume  that  at  some  previous 
time  the  corpuscle  had  absorbed  and  stored  up  from 
light  of  this  or  other  wave-length  enough  energy  sa  that 
it  needed  but  a  minute  addition  at  the  time  of  the 
experiment  to  be  able  to  be  ejected  from  the  atom  with 
the  energy  hv. 

Now  the  corpuscle  which  is  thus  ejected  by  the  light 
cannot  possibly  be  one  of  the  free  corpuscles  of  the  metal, 
for  such  a  corpuscle,  when  set  in  motion  within  a  metal, 
constitutes  an  electric  current,  and  we  know  that  such 
a  current  at  once  dissipates  its  energy  into  heat.  In 
other  words,  a  free  corpuscle  can  have  no  mechanism 
for  storing  up  energy  and  then  jerking  itself  up  "by 


234  THE  ELECTRON 

its  boot  straps"  until  it  has  the  huge  speed  of  emission 
observed. 

The  ejected  corpuscle  must  then  have  come  from  the 
inside  of  the  atom,  in  which  case  it  is  necessary  to  assume, 
if  the  Thomson-Einstein  theory  is  rejected,  that  within 
the  atom  there  exists  some  mechanism  which  will  permit 
a  corpuscle  continually  to  absorb  and  load  itself  up  with 
energy  of  a  given  frequency  until  a  value  at  least  as  large 
as  hv  is  reached.  What  sort  of  a  mechanism  this  is  we 
have  at  present  no  idea.  Further,  if  the  absorption  is 
due  to  resonance — and  we  have  as  yet  no  other  way  in 
which  to  conceive  it — it  is  difficult  to  see  how  there  can 
be,  in  the  atoms  of  a  solid  body,  corpuscles  having  all 
kinds  of  natural  frequencies  so  that  some  are  always 
found  to  absorb  and  ultimately  be  ejected  by  impressed 
light  of  any  particular  frequency.  But  apart  from  these 
difficulties,  the  thing  itself  is  impossible  if  these  absorbing 
corpuscles,  when  not  exposed  to  radiation,  are  emitting 
any  energy  at  all;  for  if  they  did  so,  they  would  in  time 
lose  all  their  store  and  we  should  be  able,  by  keeping 
bodies  in  the  dark,  to  put  them  into  a  condition  in  which 
they  should  show  no  emission  of  corpuscles  whatever 
until  after  hours  or  years  of  illumination  with  a  given 
wave-length.  Since  this  is  contrary  to  experiment,  we 
are  forced,  even  when  we  discard  the  Thomson-Einstein 
theory  of  localized  energy,  to  postulate  electronic 
absorbers  which,  during  the  process  of  absorbing,  do  not 
radiate  at  all  until  the  absorbed  energy  has  reached  a 
certain  critical  value  when  explosive  emission  occurs. 

However,  then,  we  may  interpret  the  phenomenon  of 
the  emission  of  corpuscles  under  the  influence  of  ether 
waves,  whether  upon  the  basis  of  the  Thomson-Einstein 


THE  NATURE  OF  RADIANT  ENERGY     235 

assumption  of  bundles  of  localized  energy  traveling 
through  the  ether,  or  upon  the  basis  of  a  peculiar  prop- 
erty of  the  inside  of  an  atom  which,  enables  it  to  absorb 
continuously  incident  energy  and  emit  only  explo- 
sively, the  observed  characteristics  of  the  effect  seem  to 
furnish  proof  that  the  emission  of  energy  by  an  atom  is  a 
discontinuous  or  explosive  process.  This  was  the  funda- 
mental assumption  of  Planck's  so-called  quantum  theory 
of  radiation.  The  Thomson-Einstein  theory  makes  both 
the  absorption  and  the  emission  sudden  or  explosive, 
while  the  loading  theory  first  suggested  by  Planck, 
though  from  another  view-point,  makes  the  absorption 
continuous  and  only  the  emission  explosive. 

The  h  determined  above  with  not  more  than  one- 
half  of  i  per  cent  of  uncertainty  is  the  explosive  con- 
stant, i.e.,  it  is  the  unchanging  ratio  between  the  energy 
of  emission  and  the  frequency  of  the  incident  light.  It 
is  a  constant  the  existence  of  which  was  first  discovered 
by  Planck  by  an  analysis  of  the  facts  of  black-body 
radiation,  though  the  physical  assumptions  underlying 
Planck's  analysis  do  not  seem  to  be  longer  tenable. 
For  the  American  physicists  Duane  and  Hunt1  and  Hull2 
have  recently  shown  that  the  same  quantity  h  appears 
in  connection  with  the  impact  of  corpuscles  against  any 
kind  of  a  target,  the  observation  here  being  that 
the  highest  frequency  in  the  general  or  white-light 
X-radiation  emitted  when  corpuscles  impinge  upon  a 
target  is  found  by  dividing  the  kinetic  energy  of  the 
impinging  corpuscle  by  h.  Since  black-body  radiation 
is  presumably  due  to  the  impact  of  the  free  corpuscles 
within  a  metal  upon  the  atoms,  it  is  probable  that  the 

1  Phys.  Rev.,  VI  (1915),  166.  *  Ibid.,  VII  (1916),  157. 


236  THE  ELECTRON 

appearance  of  h  in  black-body  radiation  and  in  general 
X-radiation  is  due  to  the  same  cause,  so  that,  con- 
trary to  Planck's  assumption,  there  need  not  be,  in 
either  of  these  cases,  any  coincidence  between  natural 
and  impressed  periods  at  all.  The  hv  which  here  appears 
is  not  a  characteristic  of  the  atom,  but  merely  a  property 
of  the  ether  pulse  which  is  generated  by  the  stopping  of 
a  moving  electron.  Why  this  ether  pulse  should  be 
resolvable  into  a  continuous,  or  white-light  spectrum 
which,  however,  has  the  peculiar  property  of  being 
chopped  off  sharply  at  a  particular  limiting  frequency 
given  by  hv=PDXe  is  thus  far  a  complete  mystery. 
All  that  we  can  say  is  that  experiment  seems  to  demand 
a  sufficient  modification  of  the  ether-pulse  theory  of 
white-light  and  of  general  X-radiation  to  take  this 
experimental  fact  into  account. 

On  the  other  hand,  the  appearance  of  h  in  connec- 
tion with  the  absorption  and  emission  of  monochromatic 
light  (photo-electric  effect  and  Bohr  atom)  seems  to 
demand  some  hitherto  unknown  type  of  absorbing  and 
emitting  mechanism  within  the  atom.  This  demand  is 
strikingly  emphasized  by  the  remarkable  absorbing 
property  of  matter  for  X-rays,  discovered  by  Barkla1 
and  beautifully  exhibited  in  DeBroglie's  photographs 
opposite  p.  197.  It  will  be  seen  from  these  photographs 
that  the  atoms  of  each  particular  substance  transmit  the 
general  X-radiation  up  to  a  certain  critical  frequency  and 
then  absorbs  all  radiations  of  higher  frequency  than  this 
critical  value.  The  extraordinary  significance  of  this  dis- 
covery lies  in  the  fact  that  it  indicates  that  there  is  a 
type  of  absorption  which  is  not  due  either  to  resonance  or 

*Phil.  Mag.,  XVII  (1909),  749. 


THE  NATURE  OF  RADIANT  ENERGY     237 

to  free  electrons.  But  these  are  the  only  types  of  absorp- 
tion which  are  recognized  in  the  structure  of  modern 
optics.  We  have  as  yet  no  way  of  conceiving  of  this 
new  type  of  absorption  in  terms  of  a  mechanical  model. 

There  is  one  result,  however,  which  seems  to  be 
definitely  established  by  all  of  this  experimental  work. 
Whether  the  radiation  is  produced  by  the  stopping  of  a 
free  electron,  as  in  Duane  and  Hunt's  experiments,  and 
presumably  also  in  black-body  experiments,  or  by  the 
absorption  and  re-emission  of  energy  by  bound  electrons, 
as  in  photo-electric  and  spectroscopic  work,  Planck's  h 
seems  to  be  always  tied  up  in  some  way  with  the  emis- 
sion and  absorption  of  energy  by  the  electron,  h  may 
therefore  be  considered  as  one  of  the  properties  of  the 
electron. 

The  new  facts  in  the  field  of  radiation  which  have 
been  discovered  through  the  study  of  the  properties  of 
the  electron  seem,  then,  to  require  in  any  case  a  very 
fundamental  revision  or  extension  of  classical  theories 
of  absorption  and  emission  of  radiant  energy.  The 
Thomson-Einstein  theory  throws  the  whole  burden  of 
accounting  for  the  new  facts  upon  the  unknown  nature 
of  the  ether  and  makes  radical  assumptions  about  its 
structure.  The  loading  theory  leaves  the  ether  as  it 
was  and  puts  the  burden  of  an  explanation  upon  the 
unknown  conditions  and  laws  which  exist  inside  the 
atom,  and  have  to  do  with  the  nature  of  the  electron. 
I  have  already  given  reasons  for  discrediting  the  first  type 
of  theory.  The  second  type,  though  as  yet  very  incom- 
plete, seems  to  me  to  be  the  only  possible  one,  and  it  has 
already  met  with  some  notable  successes,  as  in  the  case 
of  the  Bohr  atom.  Yet  the  theory  is  at  present  woe- 


238  THE  ELECTRON 

fully  incompjete  and  hazy.  About  all  that  we  can  say 
now  is  that  we  seem  to  be  driven  by  newly  discovered 
relations  in  the  field  of  radiation  either  to  the  Thomson- 
Einstein  semi-corpuscular  theory,  or  else  to  a  theory 
which  is  equally  subversive  of  the  established  order 
of  things  in  physics.  For  either  one  of  these  alternatives 
brings  us  to  a  very  revolutionary  quantum  theory  of 
radiation.  To  be  living  in  a  period  which  faces  such  a 
complete  reconstruction  of  our  notions  as  to  the  way  in 
which  ether  waves  are  absorbed  and  emitted  by  matter  is 
an  inspiring  prospect.  The  atomic  and  electronic  worlds 
have  revealed  themselves  with  beautiful  definiteness  and 
wonderful  consistency  to  the  eye  of  the  modern  physicist, 
but  their  relation  to  the  world  of  ether  waves  is  still  to 
him  a  profound  mystery  for  which  the  coming  generation 
has  the  incomparable  opportunity  of  finding  a  solution. 
In  conclusion  there  is  given  a  summary  of  the  most 
important  physical  constants  the  values  of  which  it  has 
become  possible  to  fix,1  within  about  the  limits  indicated, 
through  the  isolation  and  measurement  of  the  electron. 

The  electron e=  (4.774=*=  o.oo5)Xio~10 

The  Avogadro  constant N=  (6 . 062  ±  o.  006) X  io2* 

Number  of  gas  molecules  per  cc.  at 

o°C.  76  cm n=  (2.705=*=  o.oo3)XioI9 

Kinetic  energy  of  translation  of  a 

molecule  at  o°C E0=  (5.621=1=  o.oo6)Xio~I4 

Change  of   translational  molecular 

energy  per  °C e=  (2.058=*=  o.oo2)Xio~l6 

Mass  of  an  atom  of  hydrogen  in  grams  m=  (1.662=1=  o.oo2)Xio~24 

Planck's  element  of  action h=  (6.547=*=  o.oi3)Xio~27 

Wien  constant  of  spectral  radiation  C2  =  i .  43 1 2  =t  o .  0030 
Stefan-Boltzmann  constant  of  total 

radiation <r=  (5.72   ±  o.o34)Xio~12 

Grating  spacing  in  calcite d=  3.030=1=  o.ooiA 

1  SeeProc.Nat.Acad.  Sci.,  Ill  (191 7),  236;  also  Phil.  Mag.,  July,  191 7. 


APPENDIX  A 


ne  FROM  MOBILITIES  AND  DIFFUSION  COEFFICIENTS 

If  we  assume  that  gaseous  ions,  which  are  merely 
charged  molecules  or  clusters  of  molecules,  act  exactly 
like  the  uncharged  molecules  about  them,  they  will 
tend  to  diffuse  just  as  other  molecules  do  and  will  exert 
a  partial  gas  pressure  of  exactly 
the  same  amount  as  would  an 
equal  number  of  molecules  of  any 
gas.  Imagine  then  the  lower  part 
of  the  vessel  of  Fig.  30  to  be  filled 
with  gas  through  which  ions  are 
distributed  and  imagine  that  these 
ions  are  slowly  diffusing  upward. 
Let  nf  be  the  ionic  concentration, 
i.e.,  the  number  of  ions  per  cubic 
centimeter  at  any  distance  x  from 
the  bottom  of  the  vessel.  Then 
the  number  N  of  ions  which  pass 
per  second  through  i  sq.  cm.  taken  perpendicular  to  x  at 
a  distance  x  from  the  bottom  must  be  directly  propor- 
tional to  the  concentration  gradient  -j-  and  the  factor 

of  proportionality  in  a  given  gas  is  by  definition  the 
diffusion  coefficient  D  of  the  ions  through  this  gas,  i.e., 


(42) 


FIG.  30 


dx 


But  since  N  is  also  equal  to  the  product  of  the  average 
velocity  V  with  which  the  ions  are  streaming  upward  at 


239 


240  THE  ELECTRON 

x  by  the  number  of  ions  per  cubic  centimeter  at  x,  i.e., 
since  N  =n'V,  we  have  from  equation  (42) 


*  ~'    i  j     • 
n  ax 

The  force  which  is  acting  on  these  w'-ions  to  cause  this 
upward  motion  is  the  difference  in  the  partial  pressure 
of  the  ions  at  the  top  and  bottom  of  a  centimeter  cube  at 

the  point  x.    It  is,  therefore,  equal  to  -7-  dynes,  and  the 

ratio  between  the  force  acting  and  the  velocity  produced 

by  it  is 

dp 

dx 


n'  dx 

Now  this  ratio  must  be  independent  of  the  particular 
type  of  force  which  is  causing  the  motion.  Imagine  then 
the  same  w'-ions  set  in  motion,  not  by  the  process  of 
diffusion,  but  by  an  electric  field  of  strength  F.  The 
total  force  acting  on  the  w'-ions  would  then  be  Fen'  ', 
and  if  we  take  v  as  the  velocity  produced,  then  the 
ratio  between  the  force  acting  and  the  velocity  pro- 

Fen' 
duced  will  now  be  --  .     By  virtue  then  of  the  fact 

that  this  ratio  is  constant,  whatever  kind  of  force  it 
be  which  is  causing  the  motion,  we  have 

dp 

dx 


v 

n'  dx 


APPENDIX  A  241 

Now  if  v0  denote  the  velocity  in  unit  field,  a  quantity 
which  is  technically  called  the  "  ionic  mobility,"  -r,  =  v0. 
Again  since  the  partial  pressure  p  is  proportional  to  n', 

i.e.,    since   p  —  Knf,   it 
equation  (43)  reduces  to 


i.e.,    since   p  —  Knr,   it   follows   that   ^r  =  ~T-     Hence 


en  _  i 
v0  ~D 

P 
or 

v0=De— (44) 

But  if  we  assume  that,  so  far  as  all  pressure  relations 
are  concerned,  the  ions  act  like  uncharged  molecules 
(this  was  perhaps  an  uncertain  assumption  at  the  time, 
though  it  has  since  been  shown  to  be  correct),  we  have 

— =—  in  which  n  is  the  number  of  molecules  per  cubic 

centimeter  in  the  air  and  P  is  the  pressure  produced  by 
them,  i.e.,  P  is  atmospheric  pressure.  We  have_J;hen 
from  equation  (44) 

v0P  ,    , 

we=-- (45) 


APPENDIX  B 

TOWNSEND'S  FIRST  ATTEMPT  AT  A  DETER- 
MINATION OF  e 

Fig.  31  shows  the  arrangement  of  apparatus  used. 
The  oxygen  rising  from  the  electrode  E  is  first  bubbled 
through  potassium  iodide  in  A  to  remove  ozone,  then 
through  water  in  B  to  enable  the  ions  to  form  a  cloud. 
This  cloud-laden  air  then  passes  through  a  channel  in  an 
electrical  insulator — a  paraffin  block  P — into  the  tubes 


FIG.  31 


c,d,e,  which  contain  concentrated  sulphuric  acid.  These 
drying  tubes  remove  all  the  moisture  from  the  air  and 
also  such  part  of  the  charge  as  is  held  on  ions  which  in 
the  process  of  bubbling  through  c,  d,  e  have  actually 
touched  the  sulphuric  acid.  The  dry  air  containing  the 
rest  of  the  charge  passes  out  through  a  channel  in  the 
paraffin  block  P'  into  the  flask  D.  (If  the  gas  being 
studied  was  lighter  than  air,  e.g.,  hydrogen,  D  was  of 
course  inverted.)  The  outside  of  D  is  covered  with  tin 
foil  which  is  connected  to  one  of  the  three  mercury  cups 
held  by  the  paraffin  block  P" .  If  the  air  in  D  contained 

242 


APPENDIX  B  243 

at  first  no  charge,  then  an  electrical  charge  exactly 
equal  to  the  quantity  of  electricity  which  enters  the  flask 
D  will  appear  by  induction  on  the  tin-foil  coating  which 
covers  this  flask  and  this  quantity  qT  can  be  measured  by 
connecting  the  mercury  cup  2  to  cup  3  which  is  connected 
to  the  quadrant  electrometer  Q,  and  observing  the  deflec- 
tion per  minute.  Precisely  similarly  the  total  quantity 
of  .electricity  which  is  left  per  minute  in  the  drying  tubes 
Cj  d,  e  is  exactly  equal  to  the  quantity  which  appears  by 
induction  on  the  outer  walls  of  the  hollow  metal  vessel  G, 
which  surrounds  the  tubes  c,  d,  e.  This  quantity  qa  can 
be  measured  by  connecting  mercury  cup  i  to  cup  3  and 
observing  the  deflection  per  minute  of  the  quadrant 
electrometer.  The  number  of  cubic  centimeters  of  gas 
which  pass  through  the  apparatus  per  minute  is  easily 
found  from  the  number  of  amperes  of  current  which  are 
used  in  the  electrolysis  apparatus  E  and  the  electro- 
chemical equivalent  of  the  gas.  By  dividing  the  quan- 
tities of  electricity  appearing  per  minute  in  D  and  G  by 
the  number  of  cubic  centimeters  of  gas  generated  per 
minute  we  obtain  the  total  charge  per  cubic  centimeter 
carried  by  the  cloud. 

The  increase  in  weight  of  the  drying  tubes  c,  d,  e  per 
cubic  centimeter  of  gas  passing,  minus  the  weight  per 
cubic  centimeter  of  saturated  water  vapor,  gives  the 
weight  of  the  cloud  per  cubic  centimeter.  This  completes 
the  measurements  involved  in  (2)  and  (3),  p.  45. 

As  to  (4),  p.  46,  the  average  size  of  the  droplets 
of  water  Town  send  found  'by  passing  the  cloud  emerging 
from  B  into  a  flask  and  observing  how  long  it  took  for 
the  top  of  the  cloud  to  settle  a  measured  number  of 
centimeters.  The  radius  of  the  drops  could  then  be 


244  THE  ELECTRON 

obtained  from  a  purely  theoretical  investigation  made 
by  Sir  George  Stokes,1  according  to  which  the  velocity  z>j 
of  fall  of  a  spherical  droplet  through  a  gas  whose  co- 
efficient of  viscosity  was  rj  is  given  by 

v  =  2  ga?^ 
9  1°" 

in  which  a  is  the  density  of  the  droplet.  From  this 
Townsend  got  the  average  radius  a  of  the  droplets  and 
computed  their  average  weight  m  by  the  familiar  formula 

w=-7ra3<r.  He  was  then  ready  to  proceed  as  in  (5), 
see  p.  46. 

1  Lamb,  Hydronamics,  1895,  p.  533. 


APPENDIX  C 
THE  BROWNIAN-MOVEMENT  EQUATION 

A  very  simple  derivation  of  this  equation  of  Einstein 
has  been  given  by  Langevin  of  Paris1  essentially  as 
follows:  From  the  kinetic  theory  of  gases  we  have 
PV=RT=^Nmc2  in  which  c2  is  the  average  of  the  squares 
of  the  velocities  of  the  molecules,  N  the  number  of 
molecules  in  a  gram  molecule,  and  m  the  mass  of  each. 
Hence  the  mean  kinetic  energy  of  agitation  E  of  each 

~Drn 

molecule  is  given  by  E=^mc*=-  -j^-  . 

Since  in  observations  on  Brownian  movements  we 
record  only  motions  along  one  axis,  we  shall  divide  the 
total  energy  of  agitation  into  three  parts,  each  part 
corresponding  to  motion  along  one  of  the  three  axes, 

and,  placing  the  velocity  along  the  #-axis  equal  to  -rr  , 

we  have 

E 


Every  Brownian  particle  is  then  moving  about,  according 
to  Einstein's  assumption,  with  a  mean  energy  of  motion 

RT 
along  each  axis  equal  to  %-T  .    This  motion  is  due  to 


molecular   bombardment,    and   in'  order   to   write   an 

equation  for  the  motion  at  any  instant  of  a  particle 

subjected  to  such  forces  we  need  only  to  know  (i)  the 

1  Comptes  Rendtis,  CXLVI  (1908),  530. 

245 


246  THE  ELECTRON 

value  X  of  the  ^-component  of  all  the  blows  struck  by 
the  molecules  at  that  instant,  and  (2)  the  resistance 
offered  by  the  medium  to  the  motion  of  the  particle 
through  it.  This  last  quantity  we  have  set  equal  to  Kv 
and  have  found  that  in  the  case  of  the  motion  of  oil 


droplets  through  a  gas  K  has  the  value  671-170 

We  may  then  write  the  equation  of  motion  of  the  particle 
at  any  instant  uncler  molecular  bombardment  in  the  form 


d2x 


Since  in  the  Brownian  movements  we  are  interested  only 
in  the  absolute  values  of  displacements  without  regard 
to  their  sign,  it  is  desirable  to  change  the  form  of  this 


equation  so  as  to  involve  x2  and    -j-J  .    This  can  be  done 

by  multiplying  through  by  x.     We  thus  obtain,  after 

d*x  .  ,d2(x2)     /dx 

substituting  for  x       its  value  2" 


mf(#)    Jdx\_     Kd(x>) 

I ~W~m\dt)  '-  "7 ~7T+Xx (48) 


Langevin  now  considers  the  mean  result  arising  from 
applying  this  equation  at  a  given  instant  to  a  large 
number  of  different  particles  all  just  alike. 

Writing  then  z  for  -~-  in  which  x2  denotes  the  mean 

at 

of  all  the  large  number  of  different  values  of  x2,  he  gets 
after  substituting  —  for  W(^7J  »  and  remembering  that 


APPENDIX  C  247 

in  taking  the  mean,  since  the  X  in  the  last  term  is  as 
likely  to  be  positive  as  negative  and  hence  that  Xx  =  o, 

mdz    RT=     Kz 

2  dt      N  ~    ~  2  * 

Separating  the  variables  this  becomes 

dz          _K 
2RT\        m   ' 


which  yields  upon  integration  between  the  limits  o  and 
2RT 


NK 


+Ce  « (49) 


For  any  interval  of  time  r  long  enough  to  measure  this 
takes  the  value  of  the  first  term.  For  when  Brownian 
movements  are  at  all  observable,  a  is  io~4  cm.  or  less, 
and  since  K  is  roughly  equal  to  6-irrja  we  see  that, 
taking  the  density  of  the  particle  equal  to  unity, 


IQ 


-S 


K    67T.  00018X10-4 
Hence  when  r  is  taken  greater  than  about  io~s  seconds, 

-*r 

e  m  rapidly  approaches  zero,  so  that  for  any  measurable 
time  intervals 


NK 
or 


dt       NK 


248  THE  ELECTRON 

and,  letting  Ao?  represent  the  change  in  x*  in  the  time  T 

-     2RT 


( 
(50) 


This  equation  means  that  if  we  could  observe  a  large 
number  n  of  exactly  similar  particles  through  a  time  r, 
square  the  displacement  which  each  undergoes  along 
the  £-axis  in  that  time,  and  average  all  these  squared 

~Drrt 

displacements,  we  should  get  the  quantity  "TTFT.    But 

we  must  obviously  obtain  the  same  result  if  we 
observe  the  same  identical' particle  through  w-intervals 
each  of  length  T  and  average  these  w-displa cements.  The 
latter  procedure  is  evidently  the  more  reliable,  since 
the  former  must  assume  the  exact  identity  of  the 
particles. 


APPENDIX  D 


THE  INERTIA  OR  MASS  OF  AN  ELECTRICAL  CHARGE 
ON  A  SPHERE  OF  RADIUS  a 

If  Fig.  3  2  represents  a  magnet  of  pole  area  A ,  whose 
two  poles  are  d  cm.  apart,  and  have  a  total  magnetization 
M,  a  density  of  magnetization  cr,  and  a  field  strength 
between  them  of  H,  then  the  work  necessary  to  carry  a 
unit  pole  from  M  to  Mf  is  Hd,  and  the  work  necessary 
to  create  the  poles  M  and  M1 ',  i.e.,  to  carry 
M  units  of  magnetism  across  against  a 

H  .     HMd 

mean  field  strength  —  is .     Hence 

the  total  energy  Ej.  of  the  magnetic  field 
is  given  by 

=  HMd=HA<rd 


but  since  H  = 


H*Ad 

STT 


FIG.  32 


or  since  Ad  is  the  volume  of  the  field  the  energy  E  per 
unit  volume  of  the  magnetic  field  is  given  by 


H' 


(Si) 


Now  the  strength  of  the  magnetic  field  at  a  distance  r 


ev 


from  a  moving  charge  in  the  plane  of  the  charge  is  — , 

if  e  is  the  charge  and  v  its  speed.    Also  the  magnetic  field 
strength  at  a  point  distant  rd  from  the  charge,  6  being 


249 


250  THE  ELECTRON 

the  angle  between  r  and  the  direction  of  motion,  is 
given  by 


Hence  the  total  energy  of  the  magnetic  field  created  by 
the  moving  charge  is 


in  which  r  is  an  element  of  volume  and  the  integration 
is  extended  over  all  space.    But  in  terms  of  v,  6,  and  <£. 

dr=rdO,  dr,  r  sin  Od<f> 
/.     Total  energy  = 


"  (%V  =  ^ 
8'J     "  87rJ. 


Since  kinetic  energy  =Jw^,  the  mass-equivalent  m  of 
the  moving  charge  is  given  by  setting 


The  radius  of  the  spherical  charge  which  would  have  a 
mass  equal  to  the  observed  mass  of  the  negative  electron 
is  found  by  inserting  in  the  last  equation  £  =  4. 774X  io"xo 


APPENDIX  D  251 

electrostatic  units  =i. 59 iXio~ao  electromagnetic  units 

a 

and  —  =  i. 767X10'  electromagnetic,  units.     This  gives 

a=i.9Xio~13  cm. 

The  expression  just  obtained  for  m  obviously  holds 
only  so  long  as  the  magnetic  field  is  symmetrically 
distributed  about  the  moving  charge,  as  assumed  in  the 
integration,  that  is,  so  long  as  v  is  small  compared  with 
the  velocity  of  light.  When  v  exceeds  .  i  the  speed  of 
light  c,  the  mass  of  the  charge  begins  to  increase  measur- 
ably and  becomes  infinite  at  the  speed  of  light.  According 
to  the  theory  developed  by  Lorenz,  if  the  mass  for  slow 
speeds  is  called  m0  and  the  mass  at  any  speed  v  is  called 
m,  then 

m          i 

=p (53) 


This  was  the  formula  which  Bucherer  found  to  hold 
accurately  for  the  masses  of  negative  electrons  whose 
speeds  ranged  from  .  3  to  .8  that  of  light. 


APPENDIX  E 

MOLECULAR  CROSS-SECTION  AND  MEAN 
FREE  PATH 

If  there  is  one  single  molecule  at  rest  in  a  cubical 
space  i  cm.  on  a  side,  the  chance  that  another  molecule 
which  is  shot  through  the  cube  will  impinge  upon  the 

ird* 
one  contained  is  clearly  —  in  which  d  is  the  mean 

diameter  of  the  two  molecules.  If  there  are  n  contained 
molecules  the  chance  is  multiplied  by  n,  that  is,  it 

becomes .  But  on  the  average  the  chance  of  an  im- 
pact in  going  a  centimeter  is  the  number  of  impacts 
actually  made  in  traversing  this  distance.  The  mean 
free  path  /  is  the  distance  traversed  divided  by  the  num- 
ber of  impacts  made  in  going  that  distance.  Hence 


This  would  be  the  correct  expression  for  the  mean  free 
path  of  a  molecule  which  is  moving  through  a  group  of 
molecules  at  rest.  If,  however,  the  molecules  are  all  in 
motion  they  will  sometimes  move  into  a  collision  which 
would  otherwise  be  avoided,  so  that  the  collisions  will  be 
more  numerous  when  the  molecules  are  in  motion  than 
when  at  rest — how  much  more  numerous  will  depend 
upon  the  law  of  distribution  of  the  speeds  of  the  mole- 
cules. It  is  through  a  consideration  of  the  Maxwell 

252 


APPENDIX  E  253 

distribution  law  that  the  factor  V  2  is  introduced  into 
the  denominator  (see  Jeans,  Dynamical  Theory  of  Gases) 
so  that  equation  (54)  becomes 


(55) 


APPENDIX  F 

NUMBER   OF   FREE   POSITIVE   ELECTRONS    IN   THE 

NUCLEUS  OF  AN  ATOM  BY  RUTHERFORD'S 

METHOD 

If  N  represents  the  number  of  free  positive  electrons 
in  the  nucleus,  e  the  electronic  charge,  E  the  known 
charge  on  the  a-particle,  namely  2e,  and  |wFa  the 
known  kinetic  energy  of  the  a-particle,  then,  since  the 
inertias  of  the  negative  electrons  are  quite  negligible  in 
comparison  with  that  of  the  a-particle,  if  the  latter 
suffers  an  appreciable  change  in  direction  in  passing 
through  an  atom  it  will  be  due  to  the  action  of  the 
nuclear  charge.  If  b  represents  the  closest  possible 
approach  of  the  a-particle  to  the  center  of  the  nucleus, 
namely,  that  occurring  when  the  collision  is  "head  on," 
and  the  a-particle  is  thrown  straight  back  upon  its 
course,  then  the  original  kinetic  energy  \mV*  must  equal 
the  work  done  against  the  electric  field  in  approaching 
to  the  distance  b,  i.e., 


NeE  .  ,, 
(S6) 


Suppose,  however,  that  the  collision  is  not  "head  on/' 
but  that  the  original  direction  of  the  a-particle  is  such 
that,  if  its  direction  were  maintained,  its  nearest  distance 
of  approach  to  the  nucleus  would  be  p  (Fig.  33).  The 
deflection  of  the  a-particle  will  now  be,  not  180°,  as 
before,  but  some  other  angle  0.  It  follows  simply  from 

254 


APPENDIX  F 


255 


the   geometrical  properties  of  the   hyperbola  and  the 
elementary  principles  of  mechanics  that 


FIG.  33 

For  let  PAP'  represent  the  path  of  the  particle  and  let 
POA  =  6.  Also  let  V = velocity  of  the  particle  on  entering 
the  atom  and  v  its  velocity  at  A.  Then  from  the  con- 
servation of  angular  momentum 


pV=SA-v. 


(58) 


256  THE  ELECTRON 

and  from  conservation  of  energy 

NeE 
SA 


Since  the  eccentricity  e  =  sec  6,  and  for  any  conic  the  focal 
distance  is  the  eccentricity  times  one-half  the  major 
axis,  i.e.,  SO  =  OA  •  c,  it  follows  that 

SA  =  SO+OA  =So(i+H  =/>  esc  6(1+  cos  0)  =  p  cot  -  . 
But  from  equations  (58)  and  (59) 

A 


(60) 


and  since  the  angle  of  deviation  0  is  TT  —  26,  it  follows 
that 


Now  it  is  evident  from  the  method  used  in  Appen- 
dix E  that  if  there  are  n  atoms  per  cubic  centimeter 
of  a  metal  foil  of  thickness  /,  and  if  each  atom  has  a 
radius  R,  then  the  probability  M  that  a  particle  of  size 
small  in  comparison  with  R  will  pass  through  one  of 
these  atoms  in  shooting  through  the  foil  is  given  by 

M=irR2nt. 


APPENDIX  F  257 

Similarly  the  probability  m  that  it  will  pass  within  a 
distance  p  of  the  center  of  an  atom  is 


If  this  probability  is  small  in  comparison  with  unity,  it 
represents  the  fraction  p  of  any  given  number  of  particles 
shooting  through  the  foil  which  will  actually  come  within 
a  distance  p  of  the  nucleus  of  an  atom  of  the  foil. 

The  fraction  of  the  total  number  which  will  strike 
within  radii  p  and  p-\-dp  is  given  by  differentiation  as 

dm=2irpnt'dp 
but  from  equation  (57) 

#1       <£ 

^        2^    '  2 

.*.    dm=--ntb*cot-csc*-d<j>. 

4  22 

Therefore  the  fraction  p  which  is  deflected  between  the 
angles  fa  and  fa  is  given  by  integration  as 

P=-ntb2(cot2  —-cot3  — 
4       \        2  2 

It  was  this  fraction  of  a  given  number  of  a-particles 
shot  into  the  foil  which  Geiger  and  Marsden  found  by 
direct  count  by  the  scintillation  method  to  be  deflected 
through  the  angles  included  between  any  assigned  limits 
fa  and  fa.  Since  n  and  t  are  known,  b  could  be  at  once 
obtained.  It  was  found  to  vary  with  the  nature  of  the 


258  THE  ELECTRON 

atom,  being  larger  for  the  heavy  atoms  than  for  the 
lighter  ones,  and  having  a  value  for  gold  of  3 .4X  io~12  cm. 
This  is  then  an  upper  limit  for  the  size  of  the  nucleus  of 
the  gold  atom. 

As  soon  as  b  has  thus  been  found  for  any  atom, 
equation  (56)  can  be  solved  for  N,  since  E,  e,  and  \mV* 
are  all  known.  It  is  thus  that  the  number  of  free  positive 
electrons  in  the  nucleus  is  found  to  be  roughly  half  the 
atomic  weight  of  the  atom,  and  that  the  size  of  the 
nucleus  is  found  to  be  very  minute  in  comparison  with 
the  size  of  the  atom. 


APPENDIX  G 


BOHR'S  THEORETICAL  DERIVATION  OF  THE  VALUE 
OF  THE  RYDBERG  CONSTANT 

The  Newtonian  equation  of  a  circular  orbit  of  an 
electron  e  rotating  about  a  central  attracting  charge  £, 
at  a  distance  a,  with  a  rotational  frequency  n,  is 

—  =  (2irn)2ma  ................  (62) 

•p 
The  kinetic  energy  of  the  electron  is  %m(27rna)*=%  —  . 

The  work  required  to  move  the  electron  from  its  orbit 

/>  77  />  77 

to  a  position  at  rest  at  infinity  is  --  %m(27rna)2=%  —  . 

If  we  denote  this  quantity  of  energy  by  J,  it  is  seen  at 
once  that 

eE 


and 


(63) 


If  we  combine  this  with  (37),  p.  209,  there  results  at  once 


Upon  change  in  orbit  the  radiated  energy  must  be 


200  THE  ELECTRON 

and,  if  we  place  this  equal  to  hv,  there  results  the  Balmer 
formula  (34),  p.  206, 


in  which 

Since  for  hydrogen  E=e,  we  have 


and  from  (60) 


APPENDIX  H 


THE  ELEMENTS,  THEIR  ATOMIC  NUMBERS,  ATOMIC 
WEIGHTS,  AND  CHEMICAL  .POSITIONS 


iH 

1.008 


o 

I 

II 

III 

IV 

V 

VI 

VII 

VIII 

2  He 
3-90 

3  Li 
6.94 

4  Be 

Q.I 

SB 

II.  0 

6C 

12.00 

7N 
14.01 

8O 

16.00 

9F 

19.0 

10  Ne 

2O.  2 

ii  Na 
23.00 

12  Mg 

24.32 

13  Al 
27.1 

I4Si 
28.3 

15  P 

31-04 

i6S 
32.06 

17  Cl 
35.46 

18  A 
39-88 

19  K 

39.10 

20  Ca 
40.07 

21   SC 
44.1 

22  Ti 
48.1 

23V 
51-0 

24  Cr 
52.0 

25  Mn 
54  93 

26  Fe     27  Co    28  Ni 
55.84    58.97    58.68 

29  Cu 
63-57 

30  Zn 
65-37 

31  Ga 

69.9 

32  Ge 
72.5 

33  As 
74  96 

34  Se 
79  .2 

35  Br 
79  92 

36  Kr 
82.92 

37  Rb 
85-45 

38  Sr 
87-63 

HI 

40  Zr 
90.6 

41  Nb 
93-5 

42  Mo 
96.0 

43- 

44  Ru    45  Rh    46  Pd 
101.7     102.9    106.7 

47  Ag 
107.88 

48  Cd 

I  I  2  .  40 

49  In 
114.8 

50  Sn 
118.7 

Si  Sb 

1  2O.  2 

52  Te 
127.5 

53J 
126.92 

54  X 
130.2 

55  Cs 
132.81 

56  Ba 
137-37 

57  La    58  Ce    59  Pr    60  Nd   61-62  Sm  63  Eu  64  Gd  65  Tb  66  Ds 
139.0    140.25140.6    144.3          150.4     152     157.3  159  2  162.5 

67  Ho  68  Ev  69  Tu   70  Yb  71  Lu     72  — 
163.5    167.7    168.5    173.5    175-0  

73  Ta 
181.5 

74  W 
184.0 

75- 

76  Os      77  Ir     78  Pt 
190.9    193-1      195-2 



79  Au 
197.2 

80  Hg 
200.  6 

8iTl 

204.0 

82  Pb 

207.20 

83  Bi 

208.0 

84  Po 

(210.0) 

85- 

86  Em 
(222.0) 

87- 

88  Ra 
226.0 

89  Ac 
(227) 

90  Th 
232.15 

UrX2 
(234) 

92  Ur 
238.2 

Elements,  the  atomic  numbers  of  which  are  not  in  the  order  of  atomic  weights,  are  in 
italics.    The  numbers  corresponding  to  missing  elements  are  in  bold-faced  type. 


1  Hydrogen 

2  Helium 

3  Lithium 

4  Beryllium 

5  Boron 

6  Carbon 

7  Nitrogen 

8  Oxygen 

9  Fluorine 

10  Neon 

11  Sodium 

12  Magnesium 

13  Aluminium 

14  Silicon 

15  Phosphorus 

1 6  Sulphur 

17  Chlorine 

1 8  Argon 

19  Potassium 

20  Calcium 

21  Scandium 

22  Titanium 

23  Vanadium 


24  Chromium 

25  Manganese 

26  Iron 

27  Cobalt 

28  Nickel 

29  Copper 

30  Zinc 

31  Gallium 

32  Germanium 

33  Arsenic 

34  Selenium 

35  Bromine 

36  Krypton 

37  Rubidium 

38  Strontium 

39  Yttrium 

40  Zirconium 

41  Niobium 

42  Molybdenum 

44  Rhuthenium 

45  Rhodium 

46  Paladium 


47  Silver 

48  Cadmium 

49  Indium 

50  Tin 

51  Antimony 

52  Tellurium 

53  Iodine 

54  Xenon 

55  Caesium 

56  Barium 

57  Lanthanum 

58  Cerium 

59  Praseodymium 

60  Neodymium 

61  

62  Samarium 

63  Europium 

64  Gadolinium 

65  Terbium 

66  Dyprosium 

67  Holmium 

68  Erbium 

69  Thulium 


70  Ytterbium 

71  Lutecium 

72  

73  Tantalum 

74  Tungsten 

76  Osmium 

77  Indium 

78  Platinum 

79  Gold 

80  Mercury 

81  Thallium 

82  Lead 

83  Bismuth 

84  Polonium 

85  

86  Emanation 

87  

88  Radium 

89  Actinium 

90  Thorium 

91  Uranium  X» 

92  Uranium 


261 


INDEXES 


AUTHOR  INDEX 


Aepinus,  12 
Ampere,  21 
Aristotle,  9 
Arnold,  93  f. 
Avogadro,  29,  180 

Bacon,  8,  9 
Balmer,  201,  235 
Barkla,  193,  196 
Begeman,  55 
Bodoszewski,  142,  144 
Bohr,  205,  207 
Boltwood,  157 
Boltzman,  79 
Brown,  142 
Bucherer,  210 

Caertner,  115 
Carbonelle,  142 
Clausius,  8 
Coulomb,  31 
Crookes,  24 
Cunningham,  88,  160,  164 

Dalton,  2 

De  Broglie,  145,  159, 195,  I96, 
Delsaulx,  142 
Democritus,  2,  6,  9,  15 
Derieux,  176 
DeWatteville,  145,  158 
Duane,  210,  235 
Dufay,  ii 

Ehrenhaft,  145,  158  f. 
Einstein,  143,  173,  222  f. 
Elizabeth,  Queen,  n 
Enright,  44 
Epicurus,  6 
Eyring,  153 


197 


Faraday,  12,  15,  19,  28,  222  f. 

Fletcher,  127,  148!.,  161 
Franck,  37,  38,  123  f. 
Franklin,  Benjamin,  n  f.  r 

Geiger,  156,  157,  192,  193 
Gerlach,  133  f. 
Gilbert,  n 
Gilchrist,  91 
Gouy,  142  f. 

Hadamard,  87 
Harkins,  204 
Harrington,  92,  118 
Helmholtz,  22,  23,  24 
Hemsalech,  145,  158 
Hertz,  17 
Hull,  204,  235 
Hunt,  210,  235 
Huygens,  218 


133 
Joule,  7 

Karpowicz,  171 
Kaufmann,  203 
Konstaninowsky,  163 
Kelvin,  4,  23 

Ladenburg,  95 

Laue,  194 

Langevin,  35,  132,  144,  245 

Laplace,  44 

Lavoisier,  44 

Lee,J.Y,  176 

Lenard,  221,  231 

Leucippus,  2 

Lodge,  Oliver,  17,  44 

Loeb,  36 


265 


266 


THE  ELECTRON 


Lucretius,  2,  6 
Lunn,  87 
Lyman,  201,  207 

Marsden,  192,  193 
Maxwell,  8,  17.  19,  24,  79,  227 
Mendelee"ff,  200 
Meyer,  31,  133  f. 

Moseley,  193,  194,  199,  200,  201, 
202 

Newton,  207,  218 
Nordlund,  1 78 

Ostwald,  10, 154 

Paschen,  202,  206 
Perrin,  144  f.,  167 
Pierson,  134 

Planck,  115,  209,  222,  223 
Plato,  9 
Prout,  203 
Przibram,  153,  163 
Pythagoras,  4 

Ramsay,  101 

Rapp,  91 

Rayleigh,  232 

Regener,  156,  157 

Rowland,  182 

Rutherford,  Sir  Ernest,  32,  35, 156, 

192,  204,  232 
Rydberg,  214,  259 

Salles,  132 
Schidlof,  171 


Schuster,  214 
Siegbahn,  195 
Smoluchowski,  145 
Soddy,  144 
Sommerfeld,  213 
Spencer,  101 
Stokes,  46,  50,  53,  88 
Stoney,  21,  25,  31 
Sutherland,  84 
Svedberg,  147 

Thales,  i,  5,  203 

Thirion,  142 

Thomson,  Sir  J.  J.,  14,  27,  32,  34, 

40,  41,  47,  56,  68,  140,  183,  220 
Townsend,  35,  37,  38,  44,  56,  68, 

.123,  242  f. 
Tyndall,  8 

Varley,  24 

Warburg,  32 

Webster,  210 

Weiss,  150,  163 

Wellish,  36 

Westgren,  154,  178 

Westphal,  37,  38,  123  f. 

Wiechert,  40 

Wien,  44,  115 

Wilson,  C.  T.  R.;  46,  50,  132  f., 

187, 189 

Wilson,  H.  A.,  50,  52,  54,  68,  158 
Wright,  207 

Zeleny,  35 
Zerner,  163  f. 


SUBJECT  INDEX 


Absorption  and  emission  frequen- 
cies, 199 

Absorption  spectra,  196 

Alpha  particle,  range  of,  187, 
charge  of,  155  f. 

Amperian  currents,  21 

Angular  momentum,  atomicity  of, 
212 

Atom:  a  loose  structure,  191; 
diameter  of,  180;  structure  of, 
179;  the  nucleus,  190 

Atomic  numbers,  197 

Avogadro:  constant,  29;  rule,  180 

Balance:    electrical,  101;  quartz, 

101 

Balanced-drop  method,  55 
Balmer  series,  201,  206 
Black-body  radiation,  235 
Bohr  atom,  205  f. 
Brownian  movements,  10,  161  f.; 

in  gases,  143  f.;  theory  of,  245  f. 

Cavendish  Laboratory,  32,  34 
Characteristic  X-ray  spectra,  195 
Charge:  on  alpha  particle,  155  f.; 
positive  and  negative  defined,  12 
Corpuscle,  27 
Corpuscular  theory,  218  f. 

Democritus,  principles  of,  9 
Diffusion    coefficient    of    gaseous 
ions,  34  f.,  239 

e:  final  value  of,  119;  H.  A.  Wil- 
son's work  on,  52 ;  Sir  J.  J.  Thom- 
son's work  on,  47;  Townsend's 
work  on,  43,  242  f. 

Einstein's  photo-electric  equation, 
223 


Electricity:  atomic  theory  of, 
21  f.;  early  views  of,  6  f.;  Frank- 
lin's theory  of,  14;  growth  of 
theories  of,  n;  proof  of  atomic 
nature  of,  64  f.;  two-fluid  the- 
ory, 13 

Electromagnetic  theory  of  mass, 
182 

Electron:  early  values  of,  31-58; 
equality  of  positive  and  nega- 
tive, 80;  number  of,  in  atom, 
192;  origin  of  the  word,  25 

— :  Bucherer's  value  of,  210:  value 
m 

of,  in  electrolysis,  27,  30;  value 
of,  in  exhausted  tubes,  40 

Ether,  16,  218  f. 

Ether:  stress  theory,  17;  string 
theory,  222 

Explosive  emission  of  energy,  235 

Faraday  constant,  118 
Faraday's  laws,  15,  19,  28 

Gamma  rays,  221,  232 

Gaseous  conduction,  nature  of,  31 

Gram    molecule,    volume    of,    in 

gases,  30 

Grating,  molecular,  194 
Greek  philosophy,  1,9!. 

h,  value  of,  210,  227   238 
Hipp  chronoscope,  72 

Inertia  due  to  electrical  charge, 
249 

Ion,  gaseous  and  electrolytic,  33 

Ionic  charge,  74,  38 

lonization:  by  alpha  rays,  138; 
by  beta  rays,  136;  by  ether 
waves,  132;  gaseous  v.  electro- 
lytic, 39 


267 


268 


THE  ELECTRON 


Kinetic  energy  of  agitation  of  air      Orbits,    non-radiating    electronic, 
molecules  directly  observed,  78          209 


Kinetic  theory,  8,  31 
Lenard's  trigger  theory,  231 

Mass,  electrical  theory  of,  182 
Mass  of  charge  on  sphere  of  radius 
a,  249 


Periodic  table,  200,  260 
Photo-electric  effect,  221  f. 
Positive  rays,  140 

Quantum  theory,  222  f. 

Radiant  energy,  nature  of,  217  f. 


Mass,   variation  of,   with   speed,      Radium,  conductivity  in  air  due 

185,  251 

Maxwell-Boltzmann  Law,  79 
Maxwell  distribution  law,  148 


to,  32 

Radius  of  the  negative  electron, 
182,  185 


Mean  free  path  of  a  negative  elec-      Radius  of  the  positive  electron,  186 


tron,  1 88 
Mean  free  path  of  gas  molecule, 

8,  1 80,  252 

Measurement,  value  of  exact,  46      Rydberg-Schuster  law,  214 
Mechanism  of  change  of  charge, 

75 
Mechanism  of  gaseous  ionization, 

1231. 

Mobility  of  gaseous  ions,  34  f. 
Molecular  cross-section,  252 


Resistance  to  motion  independent 

of  charge,  84 
Rydberg  constant,  210,  259 


.Stokes's  Law,  46,50,  53,  144,  159  f.; 

failure  of,  89;  limits  of  validity 

of,  93 
Sub-electron,  155  f. 


Moseley's  law,  201;  inexactness  of,          I2r  f. 


Valency    in    gaseous    ionization, 


213 


Velocity    of    agitation    of    mole- 
cules, 8 


ne:  value  of,  in  electrolysis,  30;  in 

gases,  34,  239  Wave  theory,  218  f. 

Ne,  value  of,  in  electrolysis,  27  f.      Wien  constant  ca,  115,  238 
Nucleus:    atom,  190;  charge  on, 

193 


X-rays,  32 


Number  of  electrons  in  nucleus,      x'ray  spectra,  196 


254  f. 


X-ray  spectrometer,  194 


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